Answer
-3.33
Work Step by Step
We know that $\langle u_1,u_2 \rangle \cdot \langle v_1,v_2\rangle$ is equal to $u_1v_1 +u_2v_2$. The vectors are orthogonal if the dot product is zero. Thus, we find:
$$ (-3k)(2) + 5(-4) = 0 \\ 6k =-20 \\ k =-3.33$$
