mathjs/docs/reference/functions/cross.md

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.

# Function cross

Calculate the cross product for two vectors in three dimensional space.
The cross product of `A = [a1, a2, a3]` and `B =[b1, b2, b3]` is defined
as:

   cross(A, B) = [
     a2 * b3 - a3 * b2,
     a3 * b1 - a1 * b3,
     a1 * b2 - a2 * b1
   ]


## Syntax

```js
math.cross(x, y)
```

### Parameters

Parameter | Type | Description
--------- | ---- | -----------
`x` | Array | Matrix | First vector
`y` | Array | Matrix | Second vector

### Returns

Type | Description
---- | -----------
Array | Matrix | Returns the cross product of `x` and `y`


## Examples

```js
math.cross([1, 1, 0],  [0, 1, 1]);  // Returns [1, -1, 1]
math.cross([3, -3, 1], [4, 9, 2]);  // Returns [-15, -2, 39]
math.cross([2, 3, 4],  [5, 6, 7]);  // Returns [-3, 6, -3]
```


## See also

[dot](dot.md),
[multiply](multiply.md)


<!-- Note: This file is automatically generated from source code comments. Changes made in this file will be overridden. -->