Question

If $\overrightarrow{A}=3\hat{i}-4\hat{j}$ and $\overrightarrow{B}=2\hat{i}+16\hat{j}$ then the magnitude and direction of $\overrightarrow{A}+\overrightarrow{B}$ will be:-

• A. $5,{\tan }^{-1}\left(\frac{12}{5}\right)$
• B. $10,{\tan }^{-1}\left(\frac{5}{12}\right)$
• C. $13,{\tan }^{-1}\left(\frac{12}{5}\right)$
• D. $12,{\tan }^{-1}\left(\frac{5}{12}\right)$

Answer 1

The correct option is C $13,{\tan }^{-1}\left(\frac{12}{5}\right)$

$\overrightarrow{A}=3\hat{i}-4\hat{j}$
$\overrightarrow{B}=2\hat{i}+16\hat{j}$
$\therefore \overrightarrow{A}+\overrightarrow{B}=5\hat{i}+12\hat{j}$
magnitude of $\overrightarrow{A}+\overrightarrow{B}=\sqrt{5^2+{12}^2}=\sqrt{169}=13$
for direction of any vector $(a\hat{i}+b\hat{j})\to \theta ={\tan }^{-1}\frac{b}{a}$
direction of $\overrightarrow{A}+\overrightarrow{B}=\theta ={\tan }^{-1}\frac{b}{a}={\tan }^{-1}\frac{12}{5}$