Question

The magnitude of a vector which results on addition of two vectors $6\hat{i}+7\hat{j}$ and $3\hat{i}+4\hat{j}$:

• A. $\sqrt{136}$
• B. $\sqrt{132}$
• C. $\sqrt{202}$
• D. $\sqrt{160}$

Answer 1

The correct option is C $\sqrt{202}$

Let $\overrightarrow{R}=(6\hat{i}+7\hat{j})+(3\hat{i}+4\hat{j})=(9\hat{i}+11\hat{j})$
$\left|\overrightarrow{R}\right|=\sqrt{9^2+{11}^2}=\sqrt{81+121}=\sqrt{202}$