Question

Find a unit vector in the direction of the given vector.
v = 9i − 6j

Answer 1

Given:

The given vector is:

`v=9i-6j`

To find:

The unit vector in the direction of the given vector.

Solution:

If a vector is
`v=ai+bj`, then the unit vector in the direction of the this vector is

`\hat v=(v)/(|v|)`

Where,
`|v|=\sqrt{a^2+b^2`

We have,

`v=9i-6j`

Here,
`a=9` and
`b=-6`. So,

`|v|=√(9^2+(-6)^2)`

`|v|=√(81+36)`

`|v|=√(117)`

`|v|=3√(13)`

Now, the unit vector in the direction of the given vector is:

`\hat v=(9i-6j)/(3√(13))`

`\hat v=(9i)/(3√(13))-(6j)/(3√(13))`

`\hat v=(3)/(√(13))i-(2)/(√(13))j`

Therefore, the required unit vector is
`\hat v=(3)/(√(13))i-(2)/(√(13))j`.