Question

If the vectors $3\hat{i}+\lambda \hat{j}+\hat{k}\mathrm{and}2\hat{i}-\hat{j}+8\hat{k}$ are perpendicular, then λ is equal to
(a) −14
(b) 7
(c) 14
(d) $\frac{1}{7}$

Answer 1

(c) 14

$$\begin{gathered} \text{It is}\text{given that vectors}3\hat{i}+\lambda \hat{j}+\hat{k}\mathrm{and}2\hat{i}-\hat{j}+8\hat{k}\text{are perpendicular.} \\ \text{So, their dot product is zero.} \\ \left(3\hat{i}+\lambda \hat{j}+\hat{k}\right).\left(2\hat{i}-\hat{j}+8\hat{k}\right)=0 \\ \Rightarrow 6-\lambda +8=0 \\ \Rightarrow 14-\lambda =0 \\ \therefore \lambda =14 \end{gathered}$$