Answer
$90^{\circ}$
Work Step by Step
The magnitude of the vector $v$ is: $||v|| =\sqrt{1^2+1^2}=\sqrt 2$
Now, the magnitude of the vector $w$ is: $||w|| =\sqrt{2^2+(-2)^2}=2 \sqrt 2$
Thus, the distance between the terminal points is:
$d=\sqrt{(2-1)^2+(-2-1)^2}=\sqrt {10}$
Apply the law of cosines to compute the angle between the vectors.
$\cos \theta =\dfrac{(\sqrt 2)^2+(2 \sqrt 2)^2 -(\sqrt {10})^2}{2 (\sqrt 2)(\sqrt 2)}=0$
So, $\theta=90^{\circ}$
