# Overview

The cross-product is a mathematical operation you can perform on two vectors in 3D space. The cross-product produces a vector which is orthogonal to both of the input vectors, which means it is also normal to the plane containing the two input vectors.

# Mathematical Symbol

The cross product of vectors $$\textbf{a}$$ and $$\textbf{b}$$ is written as:

$$\textbf{a} \times \textbf{b}$$

# Defining Equation

The cross product is defined by the formula:

$$\textbf{a} \times \textbf{b} = ||\textbf{a}|| ||\textbf{b}|| \, sin (\theta) \, \textbf{n}$$

# Cross Product Properties

The cross product of two vector always produces a vector which:

• Is orthogonal to both input vectors (i.e. normal to the plane containing the input vectors)
• Has a direction which is determined by the right-hand rule
• Has a magnitude which is equal to the area of the parallelogram formed by the two input vectors.

Posted: February 9th, 2018 at 12:12 pm
Last Updated on: February 14th, 2018 at 5:40 am