Question

If $\overrightarrow{A}=4\hat{i}-3\hat{j}$ and $\overrightarrow{B}=6\hat{i}+8\hat{j}$ then magnitude and direction of $\overrightarrow{A}+\overrightarrow{B}$ will be

• A. $5,ta{n}^{-1}\left(\frac{3}{4}\right)$
• B. $5\sqrt{5},ta{n}^{-1}\left(\frac{1}{2}\right)$
• C. $10,ta{n}^{-1}\left(5\right)$
• D. $25,ta{n}^{-1}\left(\frac{3}{4}\right)$
  

Answer 1

The correct option is B

$5\sqrt{5},ta{n}^{-1}\left(\frac{1}{2}\right)$

$\overrightarrow{A}+\overrightarrow{B}=4\hat{i}-3\hat{j}+6\hat{i}+8\hat{j}=10\hat{i}+5\hat{j}|\overrightarrow{A}+\overrightarrow{B}|=\sqrt{(10{)}^2+(5{)}^2}=5\sqrt{5}$
$tan\theta =\frac{5}{10}=\frac{1}{2}\Rightarrow \theta =ta{n}^{-1}\left(\frac{1}{2}\right)$