Answer
$-4$, $153.4^\circ$
Work Step by Step
1. Given $\vec v=i-3j, \vec w=-i+j$, we have $\vec v\cdot\vec w=(1)(-1)+(-3)(1)=-4$
2. We can get the angle between the vectors
$\theta=cos^{-1}(\frac{\vec v\cdot\vec w}{||\vec v || ||\vec w ||})=cos^{-1}(\frac{-4}{\sqrt {1+9}\sqrt {1+19}})\approx153.4^\circ$
