Question

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

Answer 1

For the vectors to be parallel , the ratio of directions ratios should be same.
so we get $\frac{3}{1}=\frac{2}{p}=\frac{9}{3}$ , which implies $\frac{1}{p}=\frac{3}{2}$
Therefore $p=\frac{2}{3}.$