Question

If $a=2\hat{i}-\hat{j}-m\hat{k}$ and $b=\frac{4}{7}\hat{i}-\frac{2}{7}\hat{j}+2\hat{k}$ are collinear, then the value of $m$ is equal to

• A. $-7$
• B. $-1$
• C. $2$
• D. $7$
• E. $-2$

Answer 1

The correct option is A $-7$

Given $a=2\hat{i}-\hat{j}-m\hat{k}$
and $=\frac{4}{7}\hat{i}-\frac{2}{7}\hat{j}+2\hat{k}\Rightarrow b=\frac{2}{7}(2\hat{i}-\hat{j}+7\hat{k})$
Since $a$ and $b$ are collinear.
Therefore, $a=\lambda b$
$2\hat{i}-\hat{j}-m\hat{k}=\frac{2}{7}(2\hat{i}-\hat{j}+7\hat{k})$
Comparing both sides, we get
$-m=7$
$\Rightarrow m=-7$