Question

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

Answer 1

As vector $\overrightarrow{a}=3\hat{i}+2\hat{j}+9\hat{k}$ and $\overrightarrow{b}=\hat{i}-2p\hat{j}+3\hat{k}$ are parallel.

$\therefore \overrightarrow{a}=\lambda \overrightarrow{b}\Rightarrow 3\hat{i}+2\hat{j}+9\hat{k}=\lambda (\hat{i}-2p\hat{j}+3\hat{k})$

Composing coeff,
$\lambda =3,2=-2p\lambda ,9=3\lambda$

$\Rightarrow \lambda =3and2=-6p\Rightarrow p=-\frac{1}{3}$