Answer:
[tex]k=-2[/tex]Step-by-step explanation:
We have two vectors, both of which are perpendicular:
[tex]\begin{gathered} u=(-4,-8) \\ v=(2,k) \\ \text{ By the dot product definition:} \\ u\cdot v=\lvert u\rvert\lvert v\rvert\cos \theta \end{gathered}[/tex]If the vectors are perpendicular, then θ = π/2
Hence,
[tex]\begin{gathered} u\cdot v=\lvert u\rvert\lvert v\rvert\cos (\frac{\pi}{2}) \\ u\cdot v=0 \\ \text{Therefore,} \\ 0=(-4\cdot2)+(-8\cdot k) \\ 8k=-16 \\ k=-\frac{16}{8} \\ k=-2 \end{gathered}[/tex]