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. $5,ta{n}^{-1}\left(12/5\right)$
• B. $10,ta{n}^{-1}\left(5/12\right)$
• C. $20.61,ta{n}^{-1}\left(20.6/5\right)$
• D. $12,ta{n}^{-1}\left(5/12\right)$

Answer 1

The correct option is C $20.61,ta{n}^{-1}\left(20.6/5\right)$

If $\overrightarrow{A}=3\hat{i}-4\hat{j}\overrightarrow{B}=2\hat{i}-16\hat{j}$ then

the magnitude and direction

of $\overrightarrow{A}+\overrightarrow{B}$ will be

$\overrightarrow{A}+\overrightarrow{B}=(3\hat{i}-4\hat{j})+(2\hat{i}-16\hat{j})=5\hat{i}-20\hat{j}\therefore magnitude=\sqrt{25+400}=\sqrt{425}=20.61ta{n}^{-1}(-\frac{20}{5})=ta{n}^{-1}(-4)$