Question

If the scalar projection of the vector xi+j+k on the vector 2i-j+5k is $1/\surd 30$, then the value of x is?

• A. $–5/2$
• B. $6$
• C. $–6$
• D. $3$

Answer 1

The correct option is A

$–5/2$

Step 1: Given data:

if the scalar projection of the vectors $xi+j+k$ on the vector $2i-j+5k$ is $1/\surd 30$.

Step 2: Calculating the value of x

Projection of $xi+j+k$ on $2i-j+5k$

$$\begin{gathered} =\frac{\left(xi+j+k\right)\left(2i-j+5k\right)}{\sqrt{4+1+25}} \\ =\frac{2x+1+5}{\sqrt{30}} \end{gathered}$$

but $\frac{2x+6}{\sqrt{30}}=\frac{1}{\sqrt{30}}$

so, $x=-\frac{5}{2}$

Hence, the value of x is equal $-\frac{5}{2}$.