# Documentation

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# `linalg`::`crossProduct`

Cross product of three-dimensional vectors

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## Syntax

```linalg::crossProduct(`u`, `v`)
```

## Description

`linalg::crossProduct(u, v)` computes the cross product of the three-dimensional vectors and . This is the vector

.

The vectors must be defined over the same component ring.

## Examples

### Example 1

We define two vectors:

```a := matrix([[1, 2, 3]]); b := matrix([[-1, 0, 1]])```

The cross product of these two vectors is a vector which is orthogonal to and :

`c:= linalg::crossProduct(a, b)`

`linalg::scalarProduct(a, c), linalg::scalarProduct(b, c)`

## Parameters

 `u`, `v` 3-dimensional vectors, i.e., either two 3 ×1 or two 1 ×3 matrices of a domain of category `Cat::Matrix`

## Return Values

Vector of the same domain type as `u`.