If \(\vec{a} = 3\hat{\imath} - 6\hat{\jmath} + \hat{k}\) and \(\vec{b} = 2\hat{\imath} - 4\hat{\jmath} + \lambda\hat{k}\) are such that \(\vec{a}\,||\,\vec{b}\), then \(3\lambda + 2 =\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
Parallel vectors have proportional components:
\(\displaystyle \frac{2}{3} = \frac{-4}{-6} = \frac{\lambda}{1}\)
\(\displaystyle \lambda = \frac{2}{3}\)
\(3\lambda + 2 = 2 + 2 = 4\)