Answer:
[tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
Step-by-step explanation:
The unit vector for a nonzero vector, say u, in the direction of u is given by:
û = [tex]\frac{u}{|u|}[/tex] ---------------(i)
Where;
|u| = magnitude of vector u
From the question;
u = (4, -4)
First let's calculate the magnitude of u as follows;
|u| = [tex]\sqrt{(4)^2 + (-4)^2}[/tex]
|u| = [tex]\sqrt{16 + 16}[/tex]
|u| = [tex]\sqrt{32}[/tex] = [tex]4\sqrt{2}[/tex]
Now, substitute u and |u| into equation (i) as follows;
û = [tex]\frac{(4, -4)}{4\sqrt{2} }[/tex]
û = [tex](\frac{4}{4\sqrt{2} }, \frac{-4}{4\sqrt{2} } )[/tex]
û = [tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
Therefore, the unit vector is [tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
