# Unit Vector Calculator

  

An online calculator to calculate the unit vector in the direction of a vector given by its components.

## Unit Vector of a 2-D Vector

Let $\vec v$ be a vector given in component form by
$\vec v = \; \lt v_x , v_y \gt$
The unit vector $\vec {v}_u$ of vector $\vec v$ is given by
$\large \color{red} {\vec v_u = \; \lt \dfrac{v_x}{|\vec v|} , \dfrac{v_y}{|\vec v|} \gt}$
where $|\vec v|$ is the magnitude of vector $\vec v$ and is given by
$|\vec v| = \sqrt {v^2_x + v^2_y}$

## Unit Vector of a 3-D Vector

Let $\vec v$ be a vector given in component form by
$\vec v = \; \lt v_x , v_y , v_z \gt$
The unit vector $\vec {v}_u$ of vector $v$ is given by
$\large \color{red} { \vec v_u = \; \lt \dfrac{v_x}{|\vec v|} , \dfrac{v_y}{|\vec v|} , \dfrac{v_z}{|\vec v|} \gt }$
where $|\vec v|$ is the magnitude of vector $\vec v$ and is given by
$|\vec v| = \sqrt {v^2_x + v^2_y + v^2_z }$

## 2-D Unit Vector Calculator

1 - Enter the components $v_x$ and $v_y$ of vector $\vec v$ as real numbers and press "Calculate Unit Vector".

 $v_x$ = 10 , $v_y$ = -10 Decimal Places = 4 $\vec v_u$ = < , >

## 3-D Unit Vector Calculator

1 - Enter the components $v_x$, $v_y$ and $v_z$ of vector $\vec v$ as real numbers and press "Calculate Unit Vector".

 $v_x$ = 10 , $v_y$ = -10 , $v_z$ = -10 Decimal Places = 4 $\vec v_u$ = < , , >