Question

Find the value of p for which the vectors $3\hat{i}+2\hat{j}+9\hat{k}$ and $\hat{i}-2p\hat{j}+3\hat{k}$ are parallel.

Answer 1

Given are the two parallel vectors. So, their direction ratios will be proportional.

Therefore,

$\frac{3}{1}=\frac{2}{-2p}=\frac{9}{3}$

$\frac{2}{-2p}=\frac{3}{1}$

$p=-\frac{1}{3}$