# Question #5c77f

Apr 4, 2017

Option (5)

#### Explanation:

Formula to get the resolved part of a vector $\vec{V}$ along the direction making an angle $\theta$ with it is given by

${\vec{V}}_{\text{resolved part}} = \vec{V} \cos \theta$

$\vec{A}$ makes an angle $\theta = {0}^{\circ}$ with the X-axis and it makes an angle $\theta = {90}^{\circ}$ with the Y-axis.

So its resolved part along X-axis

${\vec{A}}_{x} = \vec{A} \cos {0}^{\circ}$

And its resolved part along Y-axis

${\vec{A}}_{y} = \vec{A} \cos {90}^{\circ}$

Again $\vec{B}$ makes an angle $\theta = \left({180}^{\circ} - {60}^{\circ}\right)$ with the X-axis and it makes an angle $\theta = {30}^{\circ}$ with the Y-axis.

So its resolved part along X-axis

${\vec{B}}_{x} = \vec{B} \cos \left({180}^{\circ} - {60}^{\circ}\right) = - B \cos {60}^{\circ}$

And its resolved part along Y-axis

${\vec{B}}_{y} = \vec{B} \cos {30}^{\circ}$