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

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #106 : Matrices And Vectors

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

Possible Answers:

Correct answer:

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 #2 : 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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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 #4 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector of

.

Possible Answers:

Correct answer:

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 #5 : Find The Unit Vector In The Same Direction As A Given Vector

Find the unit vector of

Possible Answers:

Correct answer:

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,

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