Given that \(\vec{a} = -3\hat{\imath}-6\hat{\jmath}+4\hat{k}, \vec{b} = 9\hat{\imath} - \lambda\hat{\jmath}-12\hat{k}\) if \(\vec{a}\times\vec{b}=\vec{0}\), then the value of \(\lambda\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → −18
For non-zero vectors, \(\vec{a}\times\vec{b} = \vec{0}\) means \(\vec{a}\) and \(\vec{b}\) are parallel, so their components are proportional:
\(\displaystyle \frac{9}{-3} = \frac{-\lambda}{-6} = \frac{-12}{4}\)
\(\displaystyle -3 = \frac{\lambda}{6}\)
\(\lambda = -18\)
Check: with \(\lambda = -18\), \(\vec{b} = 9\hat{\imath} + 18\hat{\jmath} - 12\hat{k} = -3\vec{a}\).