How to write a vector in LaTeX?

When you work online and when you create a science-related document, you need to know about latex if you want to use vector equations in that document.

There can be different types of documents. Examples are science books, research papers, online science content, and science notes, etc.

In this tutorial, we will discuss in-depth how to use latex to represent different types of vectors.

How to identify vectors with the help of latex?

Vector is always denoted by an arrow on the specified character. Here the character can be one or more.

For example, you take a vector whose initial points and final points are a and b. And you named the vector p. In this case, you can call the vector both p and ab.

You see, here ab is made up of more than one character.

So, you have to use \vec and \overrightarrow commands to vector arrow on a character in latex. And you have to pass that character as an argument in this command. Suppose I write p as a vector here.

\documentclass{article}
\begin{document}
   \[ \vec{p} \]
\end{document}

Output :

You all know about momentum which is a vector quantity. And this is product of mass and velocity.

\documentclass{article}
\begin{document}
   \[ \vec{p}=m\vec{v} \]
\end{document}

Output :

Suppose a particle travels from point A to point B, then the displacement of a particle will be

\documentclass{article}
\begin{document}
   \[ \vec{AB} \]
\end{document}

Output :

You notice the output above, vector arrow does not cover the head of whole AB. In this case, you need to use \overrightarrow command instead of \vec command.

\documentclass{article}
\begin{document}
   \[ \overrightarrow{AB} \]
\end{document}

Output :

Therefore, it is best to use \overrightarrow command when denoting a vector by more than one character.

Also, you will notice that in many books or research papers vectors are marked in bold instead of an arrow.

\documentclass{article}
\begin{document}
   \[ \textbf{AB} \]
\end{document}

Output :

That is, you need to use \textbf  command whenever you want to make a text bold.

Magnitude of a vector in latex

When the magnitude of vector is determined. Then vector is denoted in mod. So, in this case, vectors have to pass between \left | and \right | as arguments.

\documentclass{article}
\begin{document}
   \[ \left| \vec{a} \right| \]
\end{document}

Output :

Latex has many packages that you can install and use the mod easily. We have discussed here the simple method without installing any external package.

Special type of vector in latex

There are different types of vectors. Such as unit vectors, zero vectors which are denoted separately.

1. Unit Vector

We usually use a hat (^) over the vector to express unit vector in LaTeX. To show this, a carat sign is added to the name of the vector, which identifies itself as a unit vector.

\documentclass{article}
\begin{document}
   \[ \hat{a}=\frac{\vec{a}}{\left | \vec{a} \right |} \]
\end{document}

Output :

Notice the program above. To put a cap on a character, you need to pass that character in the \hat command. And for fraction, you have to use \frac command in which you have to pass two arguments as numerator and denominator.

2. Zero Vector

And for the absolute value of the vector, you know what to use as discussed in the previous point.

If the absolute value of the vector is zero then it is called a null vector or zero vector. Which is denoted with an arrow sign above zero.

Suppose the total applied force on a system is zero. In that case, the force has to be expressed in the form of a zero vector.

\documentclass{article}
\begin{document}
   \[ \vec{F}_{net}=\vec{0} \]
\end{document}

Output :

Position Vector

A position vector is represented by three rectangular unit vectors.

\documentclass{article}
\begin{document}
   \[ \vec{r}=x\hat{i}+y\hat{i}+z\hat{i} \]
\end{document}

Output :

And the \hat command is called to cap the head of each unit vector.

Vector Multiplication

Two types of products are usually seen between two vectors.

1. Cross Product in LaTeX

The cross product is denoted by a cross mark between two vectors. And its result is also a vector that is written in the form of a unit vector or matrix. And you need to use \times command to use cross mark.

\documentclass{article}
\begin{document}
   \[ \vec{p}\times \vec{q}=|\vec{p}|\vec{q}|sin\theta \hat{n} \]
\end{document}

Output :

For theta, you need to use \theta command. In which no argument has to be passed.

2. Dot Product in LaTeX

You can use dot symbols for dot products in different ways. We will use the \cdot command for vector dot product.

\documentclass{article}
\begin{document}
   \[ \vec{p}\cdot\vec{q}=|\vec{p}|\vec{q}|cos\theta \]
\end{document}

Output :

Use physics package for vector in LaTeX

In latex, physics package is defined for each special symbol or operation of physics. For example, vector arrows and vector bold are denoted by va and vb commands.

\documentclass{article}
\usepackage{physics}
\begin{document}
 \[ \va{a} \]
 \[ \va*{a} \]
 \[ \vb{a} \]
 \[ \vb*{a} \]
\end{document}

Output :

And you can easily represent all kinds of vector operations with the help of physics package. Because of this package contains pre-defined commands or functions to denote these operations. For example

\documentclass{article}
\usepackage{physics}
\begin{document}
 \[ \vu*{a} \]
 \[ \va{p}\vdot\va{q} \]
 \[ \va{p}\cp\va{q} \]
 \[ \abs{\va*{a}} \]
\end{document}

Output :