Question

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

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

Answer 1

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

Projection of $xi-j+k$ on $2i-j+5k$
$=\frac{(xi-j+k)(2i-j+5k)}{\sqrt{4+1+25}}=\frac{2x+1+5}{\sqrt{30}}$
But $\frac{2x+6}{\sqrt{30}}=\frac{1}{\sqrt{30}}$

$\Rightarrow x=-\frac{5}{2}$