Question

Find the resultant of the three vectors shown in figure and angle made by the resultant with X-axis.

• A. $\sqrt{7}4\text{m},{\tan }^{-1}\frac{7}{5}$
• B. $\sqrt{7}4\text{m},{\tan }^{-1}\frac{5}{7}$
• C. $\sqrt{8}4\text{m},{\tan }^{-1}\frac{7}{5}$
• D. None of these

Answer 1

The correct option is B $\sqrt{7}4\text{m},{\tan }^{-1}\frac{5}{7}$

We know that, the resultant vector
$R=\overrightarrow{OA}+\overrightarrow{AB}+\overrightarrow{BC}$

$R=(5\cos 37\hat{i}+5\sin 37\hat{j})+3\hat{i}+2\hat{j}$
$(\cos {37}^{\text{o}}=\frac{4}{5})$, $(\sin {37}^{\text{o}}=\frac{3}{5})$

$\Rightarrow R=4\hat{i}+3\hat{j}+3\hat{i}+2\hat{j}=7\hat{i}+5\hat{j}$

$\Rightarrow \left|R\right|=\sqrt{(7{)}^2+(5{)}^2}=\sqrt{7}4\text{m}$

The angle made by the resultant $\beta ={\tan }^{-1}\left(\frac{5}{7}\right)$
with respect to horizontal.

Hence option B is correct