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: $$ (8)(2)+(-k)(4) = 0 \\ k=4$$
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