Question

The value of $p$ for which the vectors $\overrightarrow{a}=\hat{i}-2\hat{j}-12\hat{k}$ and $\overrightarrow{b}=-3\hat{i}+6\hat{j}+p\hat{k}$ are parallel is

Answer 1

$\because \overrightarrow{a}\parallel \overrightarrow{b}$
$\Rightarrow \overrightarrow{a}=\lambda \overrightarrow{b}$
$\Rightarrow \hat{i}-2\hat{j}-12\hat{k}=\lambda (-3\hat{i}+6\hat{j}+p\hat{k})$
$\Rightarrow 1=-3\lambda ,-2=6\lambda$ and $-12=p\lambda$
$\Rightarrow \lambda =-\frac{1}{3}$
$\Rightarrow p=36$