Answer
$v \cdot w=0$
Therefore, the angle between the two vectors $v$ and $w$ is $90^{\circ}$.
Work Step by Step
We know that when the dot product between the two vectors is $0$, then they are perpendicular or orthogonal. This means that the angle between the two vectors is $90^{\circ}$.
Let us consider two vectors $v=pi+qj+rk$ and $w=xi+yj+zk$.
Then we have: $v \cdot w=(pi+qj+rk) \cdot xi+yj+zk =px+qy+rz$
In our case:
$v \cdot w=(3i-j+2k) \cdot (i+j-k) \\= (3)(1) +(-1)(1)+(2)(-1) \\=0$
Therefore, the angle between the two vectors $v$ and $w$ is $90^{\circ}$.