Question

The magnitude of the projection of the vector $\overline{a}=4\overline{i}-3\overline{j}+2\overline{k}$ on the line which makes equal angles with the coordinate axes is

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (B)

$\sqrt{3}$

Given $a=4i-3j+2k$

The line which makes equal angle with the coordinate axis is $b=i+j+k$

The projection of $a$ on $b$ is $\frac{a.b}{b}=\frac{4-3+2}{\sqrt{3}}=\frac{3}{\sqrt{3}}=\sqrt{3}$