Question

Vector$\vec { A }$ 3 its components (in terms of magnitude of $\vec { A }$) 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 $\vec { A }$ makes angles $\alpha , \beta$and $\gamma$ with x, y and z axis respectively then $\alpha = \beta = \gamma$

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

$\cos \alpha = \frac { 1 } { \sqrt { 3 } }$

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