# 3x3 Cross Product

Calculate cross product of two 3-by-1 vectors

## Library

Utilities/Math Operations

## Description

The 3x3 Cross Product block computes cross (or vector) product of two vectors, A and B, by generating a third vector, C, in a direction normal to the plane containing A and B, and with magnitude equal to the product of the lengths of A and B multiplied by the sine of the angle between them. The direction of C is that in which a right-handed screw would move in turning from A to B.

`$\begin{array}{c}A={a}_{1}i+{a}_{2}j+{a}_{3}k\\ B={b}_{1}i+{b}_{2}j+{b}_{3}k\\ C=A×B=|\begin{array}{ccc}i& j& k\\ {a}_{1}& {a}_{2}& {a}_{3}\\ {b}_{1}& {b}_{2}& {b}_{3}\end{array}|\\ =\left({a}_{2}{b}_{3}-{a}_{3}{b}_{2}\right)i+\left({a}_{3}{b}_{1}-{a}_{1}{b}_{3}\right)j+\left({a}_{1}{b}_{2}-{a}_{2}{b}_{1}\right)k\end{array}$`

## Inputs and Outputs

InputDimension TypeDescription

First

3-by-1 vector

Second

3-by-1 vector

OutputDimension TypeDescription

First

3-by-1 vector