Question

A vector $\overrightarrow{A}$ makes an angle of ${20}^0$ and $\overrightarrow{B}$ makes an angle of ${110}^0$ with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.

Answer 1

As show in figure

Angle between $\overrightarrow{A}$ and $\overrightarrow{B}={110}^0-{20}^0={90}^0$
$\overrightarrow{|A|}$ = 3 m and $\overrightarrow{|B|}$ = 4 m

Resultant,

R= $\sqrt{A^2+B^2+2ABcos\theta }$

= $\sqrt{3^2+4^2+23.4cos{90}^0}$

=5m

Let $\beta$ the angle between $\overrightarrow{R}$ and $\overrightarrow{A}$

$\beta =ta{n}^{-1}\left(\frac{4sin{90}^0}{3+4cos{90}^0}\right)$

= $ta{n}^{-1}\frac{4}{3}$

=$ta{n}^{-1}$ (1.333)

= ${53}^0$

$\therefore$ Resultant vector makes angle

= ${53}^0+{20}^0$

= ${73}^0$ with x -axis.