__maths__>__Properties of Vector Arithmetics__>__Properties of Vector Multiplication by Scalar__### Unit Vector along a vector

In this page, learn how to compute unit vector along a vector.

*click on the content to continue..*

Given the magnitude of a vector `|vec p| = 20` what is the magnitude of `(vec p)/5`?

- `20`
- `5`
- `4`
- `4`
- `1/4`

The answer is '4'. It is `(|vec p|)/(|5|)`.

Given the magnitude of a vector `|vec p|` what is the magnitude of `(vec p)/(|vec p|)`?

- 1
- 1
- `|vec p|`
- `-1`
- `-|vec p|`

The answer is '1'.

Given two vectors `vec p` and `vec q`, how can you verify if the vectors are in same direction?

- directional cosines should be equal
- directional cosines should be equal
- components along axes should be equal

The answer is 'Directional Cosines should be equal' along the respective axes.

Given two vectors `vec p` and `(vec p)/2`, are these in the same direction?

- Different directions
- Opposite directions
- Same direction
- Same direction

The answer is 'Same Direction'. Direction cosine of `(vec p)/2` is same as that of`vec p`. Please verify this by working out.

It is shown that

• magnitude of `(vec p)/(|vec p|)` is `1`

• direction of `(vec p)/(|vec p|)` is same as that of `vec p`

• Unit vector in the direction of a vector is the vector divided by its magnitude.

**Unit Vector along a Vector: ** The unit vector along a given vector `vec p` is given by

`hat p = (vec p)/(|p|)`

*Solved Exercise Problem: *

Find the unit vector along the direction of vector `vec p = 2i+2j+2k`

- `1/sqrt(3) (i+j+k)`
- `1/sqrt(3) (i+j+k)`
- `i+j+k`
- `2/sqrt(3) (i+j+k)`

The answer is '`1/sqrt(3) (i+j+k)`'.

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