Answer
$${\text{The vectors are orthogonal}}$$
Work Step by Step
$$\eqalign{
& {\bf{u}} = \left\langle {\cos \theta ,\sin \theta , - 1} \right\rangle ,{\text{ }}{\bf{v}} = \left\langle {\sin \theta , - \cos \theta ,0} \right\rangle \cr
& {\text{Find }}{\bf{u}} \cdot {\bf{v}} \cr
& {\bf{u}} \cdot {\bf{v}} = \left\langle {\cos \theta ,\sin \theta , - 1} \right\rangle \cdot \left\langle {\sin \theta , - \cos \theta ,0} \right\rangle \cr
& {\bf{u}} \cdot {\bf{v}} = \cos \theta \sin \theta - \sin \theta \cos \theta + 0 \cr
& {\bf{u}} \cdot {\bf{v}} = 0 \cr
& {\text{Therefore, the vectors are orthogonal}}{\text{.}} \cr} $$
