Question

If the vectors \[3 \hat{i} + \lambda \hat{j} + \hat{k} \text{ and } 2 \hat{i} - \hat{j} + 8 \hat{k}\] are perpendicular, then λ is equal to 

Options

• (a) −14 

• (b) 7 

• (c) 14 

• (d) \[\frac{1}{7}\] 

Answer 1

(c) 14 

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