If \( \left(\hat{\imath}+\lambda\hat{\jmath}+\mu\hat{k}\right)\times\left(2\hat{\imath}+3\hat{\jmath}+6\hat{k}\right)=\vec{0} \), then the values of \( \lambda \) and \( \mu \) are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \lambda=\displaystyle\frac{3}{2},\mu=3 \)
The cross product of two non-zero vectors is \( \vec{0} \) only when they are parallel, so their components are proportional.
\( \displaystyle \frac{1}{2}=\frac{\lambda}{3}=\frac{\mu}{6} \)
\( \displaystyle \lambda=\frac{3}{2} \)
\( \displaystyle \mu=\frac{6}{2}=3 \)