If the vectors \(2\hat{\imath}-3\hat{\jmath}+p\hat{k}\) and \(q\hat{\imath}+6\hat{\jmath}-8\hat{k}\) are collinear, then
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → p = 4, q = −4
Two vectors are collinear when one is a scalar multiple of the other, that is, when their corresponding components are proportional:
\( \displaystyle \frac{q}{2} = \frac{6}{-3} = \frac{-8}{p} \)
The middle ratio is fully known:
\( \displaystyle \frac{6}{-3} = -2 \)
So
\(q = 2\times(-2) = -4\)
\(-8 = -2p\), so \(p = 4\)