Question

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

Answer 1

If two vector$\overrightarrow{A}$ and $\overrightarrow{B}$ make an angle $\theta$ between them then resultant is

${\left(\overrightarrow{R}\right)}^2={\overrightarrow{A}}^2+{\overrightarrow{B}}^2+2\overrightarrow{A}\overrightarrow{B}cos\theta$

$\overrightarrow{A}$ and $\overrightarrow{B}$ make a angle ${20}^0$and ${110}^0$ with a x axis angle between them is ${90}^0$

${\left(\overrightarrow{R}\right)}^2={\overrightarrow{3}}^2+{\overrightarrow{4}}^2+2\times \overrightarrow{3}\times \overrightarrow{4}\times cos{90}^0=9+16+0=25$

$cos{90}^0=0$

$\Rightarrow R=\sqrt{25}=5$

angle btween $\overrightarrow{R}$ and $\overrightarrow{A}$ is ${53}^0$ so angle make by $\overrightarrow{R}$ with x axis ${53}^0+{20}^0={73}^0$

Hence the resultant is 5