Question

Find the unit vector in the direction of (4,-4). Write your answer in component form. Do not approximate any numbers in your answer.

Answer 1

`((1)/(√(2) ), (-1)/(√(2) ) )`

Explanation:

The unit vector for a nonzero vector, say u, in the direction of u is given by:

û =
`(u)/(|u|)` ---------------(i)

Where;

|u| = magnitude of vector u

From the question;

u = (4, -4)

First let's calculate the magnitude of u as follows;

|u| =
`√((4)^2 + (-4)^2)`

|u| =
`√(16 + 16)`

|u| =
`√(32)` =
`4√(2)`

Now, substitute u and |u| into equation (i) as follows;

û =
`((4, -4))/(4√(2) )`

û =
`((4)/(4√(2) ), (-4)/(4√(2) ) )`

û =
`((1)/(√(2) ), (-1)/(√(2) ) )`

Therefore, the unit vector is
`((1)/(√(2) ), (-1)/(√(2) ) )`