Question

Find component of vector $\overrightarrow{A}$ along the direction of $\overrightarrow{B}$ i.e. A||B and in perpendicular direction of $\overrightarrow{B}$ that is $A_{{\perp }_B}$.

• A. A||B = $3\sqrt{3};A\perp B=3$
• B. A||B = $\frac{3}{3};A\perp B=3\frac{\sqrt{3}}{2}$
• C. A||B = $\frac{3}{2};A\perp B=\frac{1}{2}$
• D. A||B = $\frac{3}{\sqrt{3}};A\perp B=3\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A

A||B = $3\sqrt{3};A\perp B=3$

So, we need to resolve the vector A along the direction of B and perpendicular to it.

Angle between A & B is ${30}^{\circ }$

So component along the direction B is using trigonometric ration

$6cos{30}^{\circ }$ = compound of A along B = $3\sqrt{3}$ component of A perpendicular to B = 6 $sin{30}^{\circ }$ = 3