Question

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

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

Answer 1

Answer: (A)

$\frac{A}{\sqrt{3}}$

Answer 2

Let the components of $\overset{\rightarrow}{A}$ makes angles $\alpha,\beta$and $\gamma$ with x, y and z axis respectively then $\alpha = \beta = \gamma$

$\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma = 1 \Rightarrow 3\cos^{2}\alpha = 1$ ⇒ $\cos\alpha = \frac{1}{\sqrt{3}}$

$\therefore A_{x} = A_{y} = A_{z} = A\cos\alpha = \frac{A}{\sqrt{3}}$