Answer
$${\text{The vectors are orthogonal}}{\text{}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{u}} = \left\langle {7, - 2,3} \right\rangle ,{\text{ }}{\bf{v}} = \left\langle { - 1,4,5} \right\rangle \cr
& {\text{Find }}{\bf{u}} \cdot {\bf{v}} \cr
& {\bf{u}} \cdot {\bf{v}} = \left\langle {7, - 2,3} \right\rangle \cdot \left\langle { - 1,4,5} \right\rangle \cr
& {\bf{u}} \cdot {\bf{v}} = - 7 - 8 + 15 \cr
& {\bf{u}} \cdot {\bf{v}} = 0 \cr
& {\text{Therefore, the vectors are orthogonal}}{\text{.}} \cr} $$
