Question

If the vectors $3\hat{i}+m\hat{j}+\hat{k}\mathrm{and}2\hat{i}-\hat{j}-8\hat{k}$ are orthogonal, find m.

Answer 1

$$\begin{gathered} \text{It is given that the vectors are othgonal. So, their dot product is zero.} \\ \left(3\hat{i}+m\hat{j}+\hat{k}\right).\left(2\hat{i}-\hat{j}-8\hat{k}\right)=0 \\ \Rightarrow 6-m-8=0 \\ \Rightarrow -m-2=0 \\ \Rightarrow m=-2 \end{gathered}$$