# Precalculus : Find the Unit Vector in the Same Direction as a Given Vector

## Example Questions

### Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector that is in the same direction as the vector      Explanation:

To find the unit vector in the same direction as a vector, we divide it by its magnitude.

The magnitude of is .

We divide vector by its magnitude to get the unit vector : or All unit vectors have a magnitude of , so to verify we are correct: ### Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

A unit vector has length .

Given the vector find the unit vector in the same direction.      Explanation:

First, you must find the length of the vector. This is given by the equation: Then, dividing the vector by its length gives the unit vector in the same direction. ### Example Question #3 : Find The Unit Vector In The Same Direction As A Given Vector

Put the vector in unit vector form.      Explanation:

To get the unit vector that is in the same direction as the original vector , we divide the vector by the magnitude of the vector.

For , the magnitude is:  .

This means the unit vector in the same direction of is, ### Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector of .     Explanation:

In order to find the unit vector u of a given vector v, we follow the formula Let The magnitude of v follows the formula .

For this vector in the problem    .

Following the unit vector formula and substituting for the vector and magnitude .

As such, .

### Example Question #1 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector of      Explanation:

In order to find the unit vector u of a given vector v, we follow the formula Let The magnitude of v follows the formula For this vector in the problem    Following the unit vector formula and substituting for the vector and magnitude As such, ### All Precalculus Resources 