Answer
$ 0, 90^\circ$
Work Step by Step
1. Given $\vec v=4i-j+2k, \vec w=i-2j-3k$, we have $\vec v\cdot\vec w=(4)(1)+(-1)(-2)+(2)(-3)=0$
2. We can get the angle between the vectors
$\theta=cos^{-1}(\frac{\vec v\cdot\vec w}{||\vec v || ||\vec w ||})=cos^{-1}(0)=90^\circ$
