Question

If the scalar projection of the vector $x\hat{i}-\hat{j}+\hat{k}$ on the vector $2\hat{i}-\hat{j}+5\hat{k}$ is $\frac{1}{\sqrt{30}}$, then value of $x$ is equal to

• A. $\frac{-5}{2}$ units
• B. $6$ units
• C. $-6$ units
• D. $3$ units

Answer 1

The correct option is A $\frac{-5}{2}$ units

Projection of $x\hat{i}-\hat{j}+\hat{k}$ on $2\hat{i}-\hat{j}+5\hat{k}$

$=\frac{(x\hat{i}-\hat{j}+\hat{k})(2\hat{i}-\hat{j}+5\hat{k})}{\sqrt{4+1+25}}=\frac{2x+1+5}{\sqrt{30}}$

But given,

$\frac{2x+6}{\sqrt{30}}=\frac{1}{\sqrt{30}}$
$\Rightarrow 2x+6=1$
$\Rightarrow x=\frac{-5}{2}$