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crossproductcalculator.online Ads.txt file

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Cross Product Calculator | Calculator.now</title>

<script>
(function (s, t, a, y, twenty, two) {
s.Stay22 = s.Stay22 || {};
s.Stay22.params = { lmaID: '686687a01419ac5c5acc4a42' };
twenty = t.createElement(a);
two = t.getElementsByTagName(a)[0];
twenty.async = 1;
twenty.src = y;
two.parentNode.insertBefore(twenty, two);
})(window, document, 'script', 'https://scripts.stay22.com/letmeallez.js');
</script>

<link rel="apple-touch-icon" sizes="180x180" href="/static/apple-touch-icon.png">
<link rel="icon" type="image/png" sizes="32x32" href="/static/favicon-32x32.png">
<link rel="icon" type="image/png" sizes="16x16" href="/static/favicon-16x16.png">
<link rel="icon" type="image/x-icon" href="/static/favicon.ico">
<link rel="shortcut icon" href="/static/favicon.ico">
<link rel="manifest" href="/static/site.webmanifest">

<script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-1439594428948409" crossorigin="anonymous"></script>

<script type="text/javascript" async src="https://hb-targa.s3.us-east-2.amazonaws.com/targa-calculator/calculator.now/asc_prebid.js"></script>


<script type="text/javascript" async=true>
(function() {
var host = 'calculator.now';
var element = document.createElement('script');
var firstScript = document.getElementsByTagName('script')[0];
var url = 'https://cmp.inmobi.com'
.concat('/choice/', '2MMzmDKaU6zew', '/', host, '/choice.js?tag_version=V3');
var uspTries = 0;
var uspTriesLimit = 3;
element.async = true;
element.type = 'text/javascript';
element.src = url;

firstScript.parentNode.insertBefore(element, firstScript);

function makeStub() {
var TCF_LOCATOR_NAME = '__tcfapiLocator';
var queue = [];
var win = window;
var cmpFrame;

function addFrame() {
var doc = win.document;
var otherCMP = !!(win.frames[TCF_LOCATOR_NAME]);

if (!otherCMP) {
if (doc.body) {
var iframe = doc.createElement('iframe');

iframe.style.cssText = 'display:none';
iframe.name = TCF_LOCATOR_NAME;
doc.body.appendChild(iframe);
} else {
setTimeout(addFrame, 5);
}
}
return !otherCMP;
}

function tcfAPIHandler() {
var gdprApplies;
var args = arguments;

if (!args.length) {
return queue;
} else if (args[0] === 'setGdprApplies') {
if (
args.length > 3 &&
args[2] === 2 &&
typeof args[3] === 'boolean'
) {
gdprApplies = args[3];
if (typeof args[2] === 'function') {
args[2]('set', true);
}
}
} else if (args[0] === 'ping') {
var retr = {
gdprApplies: gdprApplies,
cmpLoaded: false,
cmpStatus: 'stub'
};

if (typeof args[2] === 'function') {
args[2](retr);
}
} else {
if(args[0] === 'init' && typeof args[3] === 'object') {
args[3] = Object.assign(args[3], { tag_version: 'V3' });
}
queue.push(args);
}
}

function postMessageEventHandler(event) {
var msgIsString = typeof event.data === 'string';
var json = {};

try {
if (msgIsString) {
json = JSON.parse(event.data);
} else {
json = event.data;
}
} catch (ignore) {}

var payload = json.__tcfapiCall;

if (payload) {
window.__tcfapi(
payload.command,
payload.version,
function(retValue, success) {
var returnMsg = {
__tcfapiReturn: {
returnValue: retValue,
success: success,
callId: payload.callId
}
};
if (msgIsString) {
returnMsg = JSON.stringify(returnMsg);
}
if (event && event.source && event.source.postMessage) {
event.source.postMessage(returnMsg, '*');
}
},
payload.parameter
);
}
}

while (win) {
try {
if (win.frames[TCF_LOCATOR_NAME]) {
cmpFrame = win;
break;
}
} catch (ignore) {}

if (win === window.top) {
break;
}
win = win.parent;
}
if (!cmpFrame) {
addFrame();
win.__tcfapi = tcfAPIHandler;
win.addEventListener('message', postMessageEventHandler, false);
}
};

makeStub();

function makeGppStub() {
const CMP_ID = 10;
const SUPPORTED_APIS = [
'2:tcfeuv2',
'6:uspv1',
'7:usnatv1',
'8:usca',
'9:usvav1',
'10:uscov1',
'11:usutv1',
'12:usctv1'
];

window.__gpp_addFrame = function (n) {
if (!window.frames[n]) {
if (document.body) {
var i = document.createElement("iframe");
i.style.cssText = "display:none";
i.name = n;
document.body.appendChild(i);
} else {
window.setTimeout(window.__gpp_addFrame, 10, n);
}
}
};
window.__gpp_stub = function () {
var b = arguments;
__gpp.queue = __gpp.queue || [];
__gpp.events = __gpp.events || [];

if (!b.length || (b.length == 1 && b[0] == "queue")) {
return __gpp.queue;
}

if (b.length == 1 && b[0] == "events") {
return __gpp.events;
}

var cmd = b[0];
var clb = b.length > 1 ? b[1] : null;
var par = b.length > 2 ? b[2] : null;
if (cmd === "ping") {
clb(
{
gppVersion: "1.1", // must be “Version.Subversion”, current: “1.1”
cmpStatus: "stub", // possible values: stub, loading, loaded, error
cmpDisplayStatus: "hidden", // possible values: hidden, visible, disabled
signalStatus: "not ready", // possible values: not ready, ready
supportedAPIs: SUPPORTED_APIS, // list of supported APIs
cmpId: CMP_ID, // IAB assigned CMP ID, may be 0 during stub/loading
sectionList: [],
applicableSections: [-1],
gppString: "",
parsedSections: {},
},
true
);
} else if (cmd === "addEventListener") {
if (!("lastId" in __gpp)) {
__gpp.lastId = 0;
}
__gpp.lastId++;
var lnr = __gpp.lastId;
__gpp.events.push({
id: lnr,
callback: clb,
parameter: par,
});
clb(
{
eventName: "listenerRegistered",
listenerId: lnr, // Registered ID of the listener
data: true, // positive signal
pingData: {
gppVersion: "1.1", // must be “Version.Subversion”, current: “1.1”
cmpStatus: "stub", // possible values: stub, loading, loaded, error
cmpDisplayStatus: "hidden", // possible values: hidden, visible, disabled
signalStatus: "not ready", // possible values: not ready, ready
supportedAPIs: SUPPORTED_APIS, // list of supported APIs
cmpId: CMP_ID, // list of supported APIs
sectionList: [],
applicableSections: [-1],
gppString: "",
parsedSections: {},
},
},
true
);
} else if (cmd === "removeEventListener") {
var success = false;
for (var i = 0; i < __gpp.events.length; i++) {
if (__gpp.events[i].id == par) {
__gpp.events.splice(i, 1);
success = true;
break;
}
}
clb(
{
eventName: "listenerRemoved",
listenerId: par, // Registered ID of the listener
data: success, // status info
pingData: {
gppVersion: "1.1", // must be “Version.Subversion”, current: “1.1”
cmpStatus: "stub", // possible values: stub, loading, loaded, error
cmpDisplayStatus: "hidden", // possible values: hidden, visible, disabled
signalStatus: "not ready", // possible values: not ready, ready
supportedAPIs: SUPPORTED_APIS, // list of supported APIs
cmpId: CMP_ID, // CMP ID
sectionList: [],
applicableSections: [-1],
gppString: "",
parsedSections: {},
},
},
true
);
} else if (cmd === "hasSection") {
clb(false, true);
} else if (cmd === "getSection" || cmd === "getField") {
clb(null, true);
}
//queue all other commands
else {
__gpp.queue.push([].slice.apply(b));
}
};
window.__gpp_msghandler = function (event) {
var msgIsString = typeof event.data === "string";
try {
var json = msgIsString ? JSON.parse(event.data) : event.data;
} catch (e) {
var json = null;
}
if (typeof json === "object" && json !== null && "__gppCall" in json) {
var i = json.__gppCall;
window.__gpp(
i.command,
function (retValue, success) {
var returnMsg = {
__gppReturn: {
returnValue: retValue,
success: success,
callId: i.callId,
},
};
event.source.postMessage(msgIsString ? JSON.stringify(returnMsg) : returnMsg, "*");
},
"parameter" in i ? i.parameter : null,
"version" in i ? i.version : "1.1"
);
}
};
if (!("__gpp" in window) || typeof window.__gpp !== "function") {
window.__gpp = window.__gpp_stub;
window.addEventListener("message", window.__gpp_msghandler, false);
window.__gpp_addFrame("__gppLocator");
}
};

makeGppStub();

var uspStubFunction = function() {
var arg = arguments;
if (typeof window.__uspapi !== uspStubFunction) {
setTimeout(function() {
if (typeof window.__uspapi !== 'undefined') {
window.__uspapi.apply(window.__uspapi, arg);
}
}, 500);
}
};

var checkIfUspIsReady = function() {
uspTries++;
if (window.__uspapi === uspStubFunction && uspTries < uspTriesLimit) {
console.warn('USP is not accessible');
} else {
clearInterval(uspInterval);
}
};

if (typeof window.__uspapi === 'undefined') {
window.__uspapi = uspStubFunction;
var uspInterval = setInterval(checkIfUspIsReady, 6000);
}
})();
</script>



<meta name="description" content="
Calculate the cross product of two vectors easily with our tool. Get step-by-step solutions, accurate results, and dynamic visualizations for better understanding.
">


<meta name="robots" content="index, follow">


<link rel="canonical" href="https://calculator.now/cross-product-calculator/">


<script async src="https://www.googletagmanager.com/gtag/js?id=AW-405900530">
</script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());

gtag('config', 'AW-405900530');
</script>


<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/all.min.css" rel="stylesheet">

<script async data-id="101469123" src="//static.getclicky.com/js"></script>


<link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/css/bootstrap.min.css" rel="stylesheet">
<link rel="stylesheet" href="/static/css/styles.css">

<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/all.min.css" rel="stylesheet">

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min.js"></script>

<style>
.hidden-main {
display: none;
}
/* Ensure body and html take up the full height of the page */
html, body {
height: 100%;
margin: 0;
}

body {
max-width: 1100px;
padding: 0px !important;
margin: 0 auto !important;
display: flex !important;
flex-direction: column !important;
}

main {
flex-grow: 1;
}

.container-fluid {

padding-right: 0px !important;
padding-left: 0px !important;

}
.navbar {
width: 100%;
padding-bottom: 0;
display: flex;
justify-content: space-between;
align-items: center;
background-color: #ffffff !important;
border-bottom: 1px solid #ddd;
padding: 5px 0 0 5px !important;
}

/* Style for the burger menu icon with equal margins */
.navbar-toggler {
margin: 5px;
}

.nav-tabs {
border-bottom: none;
margin-bottom: 0;
}

.nav-tabs .nav-link {
background: linear-gradient(to bottom, #f8f9fa, white);
border: 1px solid #ddd;
border-bottom: none;
margin-right: 2px;
border-radius: 0.25rem 0.25rem 0 0;
padding: 8px 16px;
color: #555;
}

.nav-tabs .nav-link.active {
background-color: #007bff;
border-color: #007bff #007bff #fff;
color: white;
}

.nav-tabs .nav-link:hover {
background-color: #e9ecef;
}

.navbar .navbar-brand {
color: inherit;
}

footer {
max-width: 1100px;
margin: 0 auto;
text-align: left;
width: 100%;
border-top: 1px solid #ddd;
padding-top: 10px;
clear: both;
}

/* Mobile view styling */
@media (max-width: 992px) {
/* Stack the nav items vertically when in mobile view */
.nav-tabs .nav-item {
width: 100%;
}

.nav-tabs .nav-link {
display: block;
width: 100%;
text-align: left;
padding: 10px 16px;
border-radius: 0;
border: 1px solid #ddd;
margin-bottom: 2px;
}
}
</style>

<style>
/* General container styling */
#main-calculator-container {
display: flex;
}

/* Content sections for inputs and results */
.content-half {
flex: 1 1 350px;
max-width: 350px;
}

/* General container styling */
/* General container styling */
#popular-section {
background-color: beige;
border: 1px solid darkgoldenrod;
padding: 20px;
margin-top: 20px;
border-radius: 0px;
box-shadow: 0 0 10px rgba(0, 0, 0, 0.1); /* Slight shadow */
flex-basis: 350px; /* Fixed width */
flex-grow: 0; /* Prevent it from growing larger */
flex-shrink: 0; /* Prevent it from shrinking */
height: auto; /* Ensure height adjusts based on content */
margin-left: 10px; Optional: Add spacing between sections */
}

/* Remove margin-left for mobile screens */
@media (max-width: 768px) {
#main-calculator-container {
flex-direction: column;
align-items: center;
}

#popular-section {
margin-left: 0; /* Remove left margin */
width: 100%; /* Full width for mobile */
}
}

/* Tooltip styling remains unchanged */
.tooltip-container {
position: relative;
display: inline-block;
cursor: pointer;
text-decoration: underline dotted grey;
text-underline-offset: 2px; /* Adjust the space between text and the underline */
}

.tooltip-container .tooltip-text {
visibility: hidden;
width: 200px;
background-color: black;
color: #fff;
text-align: center;
border-radius: 5px;
padding: 5px 10px;
position: absolute;
z-index: 1;
bottom: 100%; /* Position above the text */
left: 50%;
margin-left: -100px;
opacity: 0;
transition: opacity 0.3s;
}

.tooltip-container:hover .tooltip-text {
visibility: visible;
opacity: 1;
}
</style>

<style>
/* Styles for the print button and date */
.header-anchor-links-left {
display: flex;
align-items: center;
gap: 10px;
margin-bottom: 3px; /* Optional: Add spacing below */
}

.header-anchor-links-left button {
flex: none !important;
width: auto !important;
background: none;
border: none;
color: inherit;
font: inherit;
text-decoration: none;
cursor: pointer;
padding: 0;
margin: 0;
display: inline-flex; /* Align icon and text horizontally */
align-items: center;
}

.header-anchor-links-left button:hover {
text-decoration: underline;
}

.header-anchor-links-left .print-date {
font-size: 14px;
color: #555; /* Optional: Different color for date */
}

/* Styles for Cite, Link, Share buttons */
.header-anchor-links-right {
display: flex;
align-items: center;
gap: 10px;
}

.header-anchor-links-right button {
flex: none !important;
width: auto !important;
background: none;
border: none;
color: inherit;
font: inherit;
text-decoration: none;
cursor: pointer;
padding: 0;
margin: 0;
display: inline-flex;
align-items: center;
}

.header-anchor-links-right button:hover {
text-decoration: underline;
}

.header-anchor-links-right | {
color: #ccc; /* Color for pipe separators */
}

/* Remove button styles and make them look like links */
.header-anchor-links button {
background: none !important; /* No background */
border: none !important; /* Remove border */
color: inherit !important; /* Use the color of the surrounding text */
font: inherit !important; /* Inherit the font from the parent element */
text-decoration: none !important; /* Remove any text decoration */
cursor: pointer !important; /* Show pointer cursor to indicate clickable element */
padding: 0 !important; /* Remove any padding */
margin: 0 !important; /* Remove any margin */
display: inline !important; /* Ensure they are inline with text */
}

/* Optional: Styling to add hover effect like links */
.header-anchor-links button:hover {
text-decoration: underline !important; /* Underline on hover to resemble links */
}

.header-hidden {
display: none !important;
}
/* Info Layer Styling */
#citeLayer {
background-color: #f8f9fa; /* Light gray background */
border: 1px solid #ccc; /* Light border */
padding: 10px; /* Add some padding */
margin-top: 10px; /* Space below the link */
border-radius: 5px; /* Rounded corners */
position: relative; /* Ensure it appears below the clicked link */
/* box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1); /* Subtle shadow for better visibility */
transition: background-color 0.3s ease;

}
/* Hide the 'X' icon when the layer is closed */
#citeLayer.hidden {
display: none;
}

.info-layer p {
margin: 0; /* Remove default margins */
}

.info-layer button {
margin-top: 5px; /* Space between text and button */
background-color: #007bff; /* Blue button */
color: white; /* White text */
border: none; /* No border */
padding: 5px 10px; /* Button padding */
border-radius: 3px; /* Rounded corners */
cursor: pointer; /* Pointer cursor */
}

.info-layer button:hover {
background-color: #0056b3; /* Darker blue on hover */
}

.grey-divider {
border: 1px solid #dddddd !important; /* Add a grey top border */
width: 100%; /* Ensure it spans the full width */
margin: 20px 0; /* Optional: Add vertical spacing */
}
/* Ensure links are inline */
.header-anchor-links {
display: flex !important; /* Use flexbox for layout */
gap: 10px !important; /* Add spacing between items */
}

.header-anchor-links a {
text-decoration: none !important; /* Remove underlines */
color: inherit !important; /* Use the parent color */
font-size: 16px !important; /* Adjust font size */
}

.header-anchor-links a:hover {
text-decoration: underline !important; /* Optional: Add underline on hover */
}
/* Cite Button Styling */
.cite-button {
margin-bottom: 10px;
}

.cite-button a {
display: inline-flex;
align-items: center;
background-color: #f8f9fa;
padding: 8px 12px;
border-radius: 5px;

text-decoration: none;
font-size: 14px;
font-weight: 500;
transition: background-color 0.2s ease;
}

.cite-button a:hover {
background-color: #e9ecef;
text-decoration: none;
}
/* Close button (X) */
.close-btn {
position: absolute;
top: 5px;
right: 8px;
cursor: pointer;
font-size: 12px;
color: #cccccc;
}

/* Styling for the copy button */
#copyButton {
display: block;
background-color: #808080; /* Default grey color */
border: none;
padding: 5px 10px;
cursor: pointer;
font-weight: bold;
border-radius: 5px;
transition: background-color 0.3s ease, color 0.3s ease;
margin-left: 0px;

}

/* When the copy button text changes to 'COPIED' */
#copyButton.copied {
background-color: #d3d3d3; /* Darker grey when clicked */
color: #fff;
}

#copyButton.hidden {
display: none !important;
}
@media (max-width: 480px) {
.last-updated {
display: none;
}
}

/* General styles for the themes list */
.themes-list {
font-family: Arial, sans-serif;
margin: 0px;
line-height: 1.4; /* Adjusted for readability */
}

/* Theme section container */
.theme-section {
margin-bottom: 0px; /* Spacing between themes */
}

/* H2 for theme titles */
.theme-section h2 {
font-size: 1.5rem; /* Slightly larger font for H2 */
font-weight: bold;
margin: 0px 0; /* Spacing above and below */
}

/* H3 for categories */
.theme-section h3 {
font-size: 1.2rem; /* Smaller than H2 */
font-weight: normal;
margin: 0; /* No additional margin */
display: inline-block; /* Ensures inline display for categories */
}

/* Links inside H2 and H3 */
.theme-section h2 a,
.theme-section h3 a {
text-decoration: none; /* Remove underline */
}

.theme-section h2 a:hover,
.theme-section h3 a:hover {
text-decoration: underline; /* Add underline on hover for accessibility */
}

/* Hidden-main class styling */
.hidden-main {
font-size: 0.9rem; /* Slightly smaller for the extra text */
color: #777; /* Muted text color */
font-weight: normal;
}

/* TWO COLUMN IN CATEGORY */
.calculators-two-col {

margin-bottom: 0.5rem;
}

.calculators-two-col ul {
/* Enable bullet points */
list-style-type: disc;

/* Provide space for bullets */
margin: 0;

/* Single column by default (mobile) */
column-count: 1;
column-gap: 1rem;
}

.calculators-two-col ul li {
}

/* For desktop screens */
@media (min-width: 768px) {
.calculators-two-col ul {
column-count: 2; /* Switch to two columns on larger screens */
}
}

/* --- START: Add/Modify these styles for Search --- */

/* Style for the full-width search bar below the nav */
#full-width-search-bar {
/* Visible by default on larger screens, hidden on mobile via media query */
padding: 15px 10px;
background: linear-gradient(to bottom, white, #f8f9fa);
border-bottom: 1px solid #ddd;
margin-bottom: 0px; /* Optional spacing below search bar */
}
#full-width-search-bar .input-group .btn {
flex-shrink: 0; /* Prevent button shrinking */
}

/* Container for mobile search in dropdown */
.mobile-search-container {
display: none; /* Hidden by default, shown on mobile via media query */
padding: 10px 15px; /* Spacing within the dropdown */
}
.mobile-search-container input {
width: 100%;
padding: 8px 12px;
border: 1px solid #ccc;
border-radius: 0.25rem;
}

/* Responsive adjustments - MODIFY existing @media query */
@media (max-width: 991.98px) { /* Match Bootstrap LG breakpoint */
/* Keep existing mobile styles for .nav-tabs .nav-item and .nav-tabs .nav-link */
.nav-tabs .nav-item {
width: 100%;
}
.nav-tabs .nav-link {
display: block;
width: 100%;
text-align: left;
padding: 10px 16px;
border-radius: 0;
border: 1px solid #ddd;
margin-bottom: -1px; /* Overlap borders slightly */
margin-right: 0;
white-space: normal; /* Allow text wrapping in mobile tabs */
}
.nav-tabs .nav-link.active {
/* Ensure active border is visible if needed, e.g.: */
border-color: #007bff;
}

/* ADD these rules inside this existing media query */
#full-width-search-bar {
display: none !important; /* Hide desktop bar on mobile */
}
.mobile-search-container {
display: block !important; /* Show mobile bar in dropdown */
}
}

/* ADD this new media query for desktop */
@media (min-width: 992px) {
/* Hide mobile search container on desktop */
.mobile-search-container {
display: none !important;
}
/* Ensure desktop search bar is visible (optional reinforcement) */
#full-width-search-bar {
display: block; /* Or flex if using flex layout inside */
}
}
/* --- END: Add/Modify these styles for Search --- */

.mobile-search-container .input-group .btn.btn-outline-secondary {
border-color: #ced4da !important; /* Match default form-control border color. Use !important to be sure. */
}

/* Optional: Keep border color consistent on hover too */
/* If you want the border to stay light grey even when hovering over the button */
/* Remove this block if you prefer the button border to darken on hover */
.mobile-search-container .input-group .btn.btn-outline-secondary:hover {
border-color: #ced4da !important;
/* Keep default hover background/text for visual feedback */
color: #fff;
background-color: #6c757d;
}

/* --- Styles for Nav Text (New/Blog) --- */

/* By default (which applies to desktop), hide the text part */
.nav-text-mobile-only {
display: none;
}

/*
When the navbar is collapsed (mobile view) AND the menu (#themeMenu) is expanded (has class .show),
then display the text.
We target screens up to the point Bootstrap collapses the navbar-expand-lg (991.98px).
*/
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<h1>Cross Product Calculator</h1>

<span class="print-date" style="margin-bottom:3px;">Category: <a href="/categories/linear-algebra/">Linear Algebra</a></span>

<span class="print-date" style="margin-bottom:3px;">
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Author: <a href="https://www.linkedin.com/in/henrick-yau/" rel="nofollow" target="_blank" style="text-decoration: none; color: inherit;">Henrick Yau</a>
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Cross Product Calculator - Available at:
<a href="https://calculator.now/cross-product-calculator/" target="_blank">https://calculator.now/cross-product-calculator/</a>
- Accessed: September 09, 2025. Author: Henrick Yau.
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Cross Product Calculator - Available at:
<a href="https://calculator.now/cross-product-calculator/" target="_blank">https://calculator.now/cross-product-calculator/</a>
- Accessed: September 09, 2025. Author: Henrick Yau.
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width: 100px;
padding: 5px;
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border: 1px solid #ccc;
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margin-bottom: 20px;
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<div id="custom-calculator-container" class="custom-calculator-box">
<div id="custom-calculator-inputs">
<h3>Vector a</h3>
<label>x: <input type="number" id="vector-a-x" /></label>
<label>y: <input type="number" id="vector-a-y" /></label>
<label>z: <input type="number" id="vector-a-z" /></label>
<h3>Vector b</h3>
<label>x: <input type="number" id="vector-b-x" /></label>
<label>y: <input type="number" id="vector-b-y" /></label>
<label>z: <input type="number" id="vector-b-z" /></label>
<button id="custom-calculator-calculate-btn">Calculate</button>
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<div id="custom-calculator-results">
<h3>Cross Product Result:</h3>
<p id="cross-product-output"></p>
<div id="custom-calculator-steps"></div>
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</div>
</div>

<script src="https://cdn.jsdelivr.net/npm/chart.js"></script>



<script>
document.getElementById("custom-calculator-calculate-btn").addEventListener("click", function () {
// Get input values
const ax = parseFloat(document.getElementById("vector-a-x").value);
const ay = parseFloat(document.getElementById("vector-a-y").value);
const az = parseFloat(document.getElementById("vector-a-z").value);
const bx = parseFloat(document.getElementById("vector-b-x").value);
const by = parseFloat(document.getElementById("vector-b-y").value);
const bz = parseFloat(document.getElementById("vector-b-z").value);

// Calculate cross product
const cx = ay * bz - az * by;
const cy = az * bx - ax * bz;
const cz = ax * by - ay * bx;

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document.getElementById("cross-product-output").innerHTML = `
<strong>Cross Product:</strong> (${cx}, ${cy}, ${cz})
`;

// Show calculation steps
const steps = `
<strong>Steps to Calculate:</strong>
<ol>
<li>Use the formula:
<br>(<em>ay × bz - az × by</em>, -(<em>ax × bz - az × bx</em>), <em>ax × by - ay × bx</em>)</li>
<li>Substitute values:
<br>(${ay} × ${bz} - ${az} × ${by}, -(${ax} × ${bz} - ${az} × ${bx}), ${ax} × ${by} - ${ay} × ${bx})</li>
<li>Simplify each component:
<br>x: ${ay} × ${bz} - ${az} × ${by} = ${ay * bz} - ${az * by} = ${cx}
<br>y: -(${ax} × ${bz} - ${az} × ${bx}) = -(${ax * bz} - ${az * bx}) = ${-cy}
<br>z: ${ax} × ${by} - ${ay} × ${bx} = ${ax * by} - ${ay * bx} = ${cz}</li>
</ol>
`;
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stepsElement.innerHTML = steps;
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type: "scatter",
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datasets: [
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label: "Vector a",
data: [{ x: 0, y: 0 }, { x: ax, y: ay }],
borderColor: "blue",
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data: [{ x: 0, y: 0 }, { x: bx, y: by }],
borderColor: "green",
showLine: true,
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borderColor: "red",
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title: { display: true, text: "X-axis" },
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<div id="additional-output" class="mt-4">

<h2>Cross Product Calculator: Understanding and Using It</h2>
<p>The <strong>Cross Product Calculator</strong> is a powerful tool designed to help you compute the cross product of two three-dimensional vectors effortlessly. This calculator not only provides the result but also offers step-by-step guidance on how the calculation is performed, making it an essential resource for students, professionals, and enthusiasts working with vector <a href="/themes/mathematics/">Mathematics</a>.</p>
<h2>What Is a Cross Product?</h2>
<p>The <strong>cross product</strong> is a mathematical operation performed on two vectors in three-dimensional space. It results in a new vector that is perpendicular to both input vectors. This is particularly useful in fields such as <a href="/categories/physics/">Physics</a>, engineering, and computer graphics, where it is essential to find vectors that represent directions or orientations.</p>
<h3>Key Properties of the Cross Product:</h3>
<ul>
<li>The result is always a vector, not a scalar.</li>
<li>The magnitude of the resulting vector represents the area of the parallelogram formed by the two input vectors.</li>
<li>The direction of the resulting vector is determined by the <strong>right-hand rule</strong>.</li>
</ul>
<h2>How to Use the Cross Product Calculator</h2>
<p>Follow these steps to use the calculator effectively:</p>
<h3>1. Input Your Vectors</h3>
<ul>
<li>Enter the <strong>x</strong>, <strong>y</strong>, and <strong>z</strong> components of the first vector (<strong>Vector a</strong>) in the respective input fields.</li>
<li>Similarly, enter the <strong>x</strong>, <strong>y</strong>, and <strong>z</strong> components of the second vector (<strong>Vector b</strong>).</li>
</ul>
<h3>2. Calculate</h3>
<ul>
<li>Click the <strong>"Calculate"</strong> button. The calculator will instantly compute the cross product and display the result in vector form (e.g., <code>(x, y, z)</code>).</li>
</ul>
<h3>3. View the Steps</h3>
<ul>
<li>The calculator breaks down the cross product computation step by step:</li>
<li><strong>The Formula</strong>: Displays the mathematical formula used.</li>
<li><strong>Substitutions</strong>: Shows how your inputs are substituted into the formula.</li>
<li><strong>Simplification</strong>: Provides the calculated values for each component of the result.</li>
</ul>
<h3>4. Visualize the Result</h3>
<ul>
<li>A dynamic graph is generated to visualize the input vectors and their cross product. This helps you understand the geometric relationship between the vectors.</li>
</ul>
<h2>Example Calculation</h2>
<p>Suppose you want to find the cross product of the vectors:</p>
<ul>
<li><strong>Vector a</strong> = (3, 4, 5)</li>
<li><strong>Vector b</strong> = (2, -1, 3)</li>
</ul>
<h3>Steps to Solve:</h3>
<ol>
<li>
<p><strong>Apply the Formula</strong>:<br />
To find the cross product of two vectors, use the formula:<br />
<code>Cross Product = (ay × bz - az × by, -(ax × bz - az × bx), ax × by - ay × bx)</code></p>
</li>
<li>
<p><strong>Insert the Values</strong>:<br />
Substitute the components of the vectors into the formula:<br />
<code>(4 × 3 - 5 × -1, -(3 × 3 - 5 × 2), 3 × -1 - 4 × 2)</code></p>
</li>
<li>
<p><strong>Solve Each Component</strong>:<br />
Perform the calculations for each coordinate step-by-step: </p>
</li>
<li>x-coordinate: <code>4 × 3 - 5 × -1 = 12 + 5 = 17</code> </li>
<li>y-coordinate: <code>-(3 × 3 - 5 × 2) = -(9 - 10) = 1</code> </li>
<li>
<p>z-coordinate: <code>3 × -1 - 4 × 2 = -3 - 8 = -11</code></p>
</li>
<li>
<p><strong>Final Result</strong>:<br />
Combine the components to form the cross product vector:<br />
<code>Cross Product = (17, 1, -11)</code></p>
</li>
</ol>
<h2>Benefits of Using the Calculator</h2>
<ul>
<li><strong>Time-Saving</strong>: Quickly computes results that would otherwise take time to calculate manually.</li>
<li><strong>Accurate</strong>: Eliminates the possibility of manual calculation errors.</li>
<li><strong>Educational</strong>: Offers step-by-step solutions, helping users learn and understand the calculation process.</li>
<li><strong>Interactive Visualization</strong>: Displays the vectors and their cross product graphically for better comprehension.</li>
</ul>
<h2>Applications of the Cross Product</h2>
<p>This calculator is useful in various applications, including:
- <strong>Physics</strong>: Calculating torque, angular momentum, or magnetic force.
- <strong>Engineering</strong>: Determining directions perpendicular to surfaces or forces.
- <strong>Computer Graphics</strong>: Calculating normals for surfaces and 3D modeling.
- <strong>Robotics</strong>: Determining rotational vectors or directions.</p>
<h2>Why Choose This Calculator?</h2>
<ul>
<li><strong>User-Friendly Interface</strong>: Simplified inputs and clear outputs make it easy for anyone to use.</li>
<li><strong>Step-by-Step Solutions</strong>: Perfect for students or anyone looking to understand the process behind the calculation.</li>
<li><strong>Dynamic Graphing</strong>: Visualize vectors and their relationships directly within the tool.</li>
</ul>
<p>Whether you're solving physics problems, designing 3D models, or simply exploring vector math, the Cross Product Calculator is here to make your work easier and more intuitive.</p>

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Calculate the cross product of two vectors easily with our tool. Get step-by-step solutions, accurate results, and dynamic visualizations for better understanding.

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