If the vectors \(\vec{a} = 3\hat{\imath} - p\hat{\jmath} + 5\hat{k}\) and \(\vec{b} = -6\hat{\imath} + 14\hat{\jmath} + q\hat{k}\) are collinear, then the value of \(p\) and \(q\) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(p = 7, q = -10\)
Collinear vectors are scalar multiples of each other: \(\vec{b} = \lambda\vec{a}\). Comparing components:
\(-6 = 3\lambda,\quad \lambda = -2\)
\(14 = \lambda(-p) = 2p,\quad p = 7\)
\(q = 5\lambda = -10\)