$k=-2$ or $k=3$
Work Step by Step
We know that two vectors are orthogonal if their dot product is $0$. Hence: $u\cdot v=1\cdot k^2-1\cdot k+2\cdot(-3)=0\\k^2-k-6=0\\(k+2)(k-3)=0$ Thus: $k=-2$ or $k=3$
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