How to create a cross product symbol in LaTeX

# How to create a cross product symbol in LaTeX

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This article aims to show you a simple way to create a cross product symbol in LaTeX.

LaTeX most of the time is used to write documents that include many mathematics operations and procedures. And when dealing with vectors, in algebra or calculus, the cross product surely will be there.

We will discuss how to write cross-product symbols in LaTeX. A cross-product symbol is sometimes referred to as a vector product in LaTeX.

## LaTeX Cross Product Command

The cross product of two vectors is operation between denoted by an X, which results in a third orthogonal vector to the other two. Both vectors must have the same size usually in a 3-D space.

Denoted as x, a multiplication symbol, the command for the cross product is \times, it does not require extra packages or arguments, the use of the amsmath package to improve the output is optional, and the math mode is required. For example

\documentclass{article}
\usepackage{amsmath}
\begin{document}

$$\vec{a}\times\vec{b}$$ %times

\end{document}


With the /vec{} command, you can specify one single character and it will be returned with an arrow mark on top of it.

We need to use the /vec{} command in the equation before the variable or value in curly brackets to represent the variable or integer value in the vector. To transform the values “x” and “b” to vectors, we’ve inserted the /vec{} command before and after the “times” instruction.

## Cross Product – Unit Vector

The first form of the cross product is with a unit vector, to generate the vector output, you use the \vec{} command. For example

\begin{document}

$$\vec{a}\times\vec{b} =|a||b|\sin \theta\hat{n}$$ %times character
\end{document}


A single character is passed as argument to the /vec{a} command and is returned with an arrow mark.

The angle between the a and b is denoted by (theta), the unit vector perpendicular to a, b by \hat{}.

When you are writing the vector product in LaTeX, depending on the mathematics involved you have two options.

## Cross Product – Matrix Form

Basically the Cross Product has two forms related to its Matrix form therefore it has two LaTeX commands available. To define it with matrices you will need the latex commands for the \pmatrix and \vmatrix environment and the amsmath package.

The first form with \vmatrix environment is usually used with determinants. For example you can write

...
$$\begin{vmatrix} %matrix used for determinants \hat{i} & \hat{j} & \hat{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}$$
...


Gives the output

The & defines each column and \\ represent each row or line for any element. Now you can defined the cross product as

$$\vec{a} \times \vec{b} = \begin{vmatrix} i & j & k \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix} = (a_{2}b_{3}-a_{3}b_{2})i + (a_{3}b_{}1-a_{1}b_{3})j+ (a_{1}b_{2}-a_{2}b_{1})k$$


Gives the output

## Cross product – Parenthesis form

The second form is a matrix with parenthesis defined by the \pmatrix environment. For example

\begin{center}

Given$\vec{a}=\begin{pmatrix} a_{1}\\ a_{2}\\ a_{3} \end{pmatrix}$ and $\vec{b}=\begin{pmatrix} b_{1}\\ b_{2}\\ b_{3} \end{pmatrix}$.
$\vec{a} \times \vec{b}$ is defined as:
$\vec{a} \times \vec{b} = (a_{2}b_{3}-a_{3}b_{2})i + (a_{3}b_{}1-a_{1}b_{3})j + (a_{1}b_{2}-a_{2}b_{1})k$

\end{center}


parenthesis matrix form

The \\  commands define each line of the elements in the parenthesis matrix form.

Since it is built-in in LaTeX, don’t try to complicate the code with packages for this symbol.

Now you know its definition, how to represent this multiplication symbol, how to work with cross products and the two forms it has to insert in your LaTeX code.

I hope this post was helpful in guiding you using the wonderful tool that LaTeX is, and as always, keep writing in LaTeX. 