Question

Find the resultant of the three vectors shown in figure

Answer 1

$\overrightarrow{A}=5cos{37}^0\hat{i}+5sin{37}^0\hat{j}$

$\overrightarrow{B}=3\hat{i}$

$\overrightarrow{C}=2\hat{j}$

$\overrightarrow{R}=(5cos{37}^0+3)\hat{i}+(5sin{37}^0+2)\hat{j}$

$=(5\times \frac{4}{5}+3)\hat{i}+(5\times \frac{3}{5}+2)\hat{j}$

$=(4+3)\hat{i}+(3+2)\hat{j}$

$\overrightarrow{R}=7\hat{i}+5\hat{j}$

$|\overrightarrow{R}|=\sqrt{7^2+5^2}$

$=\sqrt{49+25}$

$=\sqrt{74}=8.6m$