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

Answer:

$(\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )$

Step-by-step explanation:

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

û = $\frac{u}{|u|}$             ---------------(i)

Where;

|u| = magnitude of vector u

From the question;

u = (4, -4)

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

|u| = $\sqrt{(4)^2 + (-4)^2}$

|u| = $\sqrt{16 + 16}$

|u| = $\sqrt{32}$ = $4\sqrt{2}$

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

û = $\frac{(4, -4)}{4\sqrt{2} }$

û = $(\frac{4}{4\sqrt{2} }, \frac{-4}{4\sqrt{2} } )$

û = $(\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )$

Therefore, the unit vector is $(\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )$