How to define unit vector(â ) in LaTeX?

To define a unit vector with the help of latex, you need to be familiar with these three symbols given below.

Vector
\vec
Hat \hat
absalute value
\left | …\right |

Because the unit vector is identified by the above three symbols.

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

Output :

define unit vector symbol

Rectangular unit vector components in LaTeX

The common three Rectangular unit vectors are marked with a cap symbol above the i, j and k symbol.

\documentclass{article}
\begin{document}
   $$ \left ( \hat{i},\hat{j},\hat{k} \right ) $$
\end{document}

Output :

Rectangular unit vector

In 3D space, the vector is always written as Rectangular unit vector.

\documentclass{article}
\begin{document}
   $$ \vec{r}=x\hat{i}+y\hat{j}+z\hat{k} $$
\end{document}

Output :

position

For example, when defining a unit vector of a vector, it will be shaped

\documentclass{article}
\begin{document}
   $$ \hat{r}=\frac{x\hat{i}+y\hat{j}+z\hat{j}}{\sqrt{x^{2}+y^{2}+z^{2}}} $$
\end{document}

Output :

unit vector from position vector

In many high level physics books you will see that ex, ey and ez are used for rectangular unit vectors without using i, j and k.

\documentclass{article}
\begin{document}
   $$ \left ( \hat{i},\hat{j},\hat{k} \right ) $$
\end{document}

Output :

ex, ey and ez

All the commands used so far have been used in the program by default. And no external packages were installed.

You can install physics packages to define this unit vector in latex. Which contain \vu*{} command for unit vector symbol.

\documentclass{article}
\usepackage{physics}
\begin{document} 
   $$\vu*{a}=\frac{\va*{a}}{\abs{\va*{a}}}$$   
\end{document}

Output :

unit vector define by latex physics package

Notice the latex program above. \va*{} and \abs{} commands are used for vector and absolute value symbols.

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