Answer
$\left( {\frac{3}{2}\sqrt 2 , - \frac{3}{2}\sqrt 2 } \right)$
Work Step by Step
We have the angle of the vector $\frac{{7\pi }}{4}$. Notice that the vector is in the fourth quadrant. The length of the vector is $3$. So, the coordinates of the vector:
$x = 3\cos \frac{{7\pi }}{4} = \frac{3}{2}\sqrt 2 $
$y = 3\sin \frac{{7\pi }}{4} = - \frac{3}{2}\sqrt 2 $
The position vector is $\left( {\frac{3}{2}\sqrt 2 , - \frac{3}{2}\sqrt 2 } \right)$.
