Question

Find the value of λ if the vectors \[2 \hat{i} + \lambda \hat{j} + 3 \hat{k} \text{ and } 3 \hat{i} + 2 \hat{j} - 4 \hat{k}\] are perpendicular to each other. 

Answer 1

\[\text{ Given }: 2 \hat{i} + \lambda \hat{j} + 3 \hat{k} \text{ and } 3i + 2j - 4k \text{ are perpendicular to each other } . \]

\[\text{ So, their dot product is zero }.\]

\[\left( 2 \hat{i} + \lambda \hat{j} + 3 \hat{k} \right) . \left( 3i + 2j - 4k \right)\]

\[ \Rightarrow 6 + 2\lambda - 12 = 0\]

\[ \Rightarrow 2\lambda - 6 = 0\]

\[ \Rightarrow \lambda = 3\]