Question

Vector $\overrightarrow{A}$ makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of $\overrightarrow{A}$) will be

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

Answer 1

The correct option is A $\frac{A}{\sqrt{3}}$

Let the components of $\overrightarrow{A}$ makes angles $\alpha ,\beta$ and
$\gamma$ with x, y and z axis respectively then $\alpha =\beta =\gamma$
$co{s}^2\alpha +co{s}^2\beta +co{s}^2\gamma =1$
$\Rightarrow 3co{s}^2\alpha =1\Rightarrow cos\alpha =\frac{1}{\sqrt{3}}$
$\therefore A_x=A_y=A_z=Acos\alpha =\frac{A}{\sqrt{3}}$.