Answer
$v \cdot w=0$
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 $90^{\circ}$. 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:
$v \cdot w=\lt 1,-1, 0 \gt \cdot \lt 1,1,1 \gt= (1)(1) +(-1)(1)+(0)(1) \\=0$
Thus, the two vectors are orthogonal and the angle between them is $90^{\circ}$.
