Question

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

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

Answer 1

The correct option is D

$\sqrt{202}$

Explanation of the correct option.

Compute the magnitude:

Let us assume $A=6\hat{i}+7\hat{j}$, $B=3\hat{i}+4\hat{j}$

Add both the vectors,

$$\begin{gathered} A+B=\left(6\hat{i}+7\hat{j}\right)+\left(3\hat{i}+4\hat{j}\right) \\ \Rightarrow A+B=9\hat{i}+11\hat{j} \end{gathered}$$

The magnitude of the addition of the vectors,

$$\begin{gathered} \left|A+B\right|=\sqrt{9^2+{11}^2} \\ \Rightarrow \left|A+B\right|=\sqrt{81+121} \\ \Rightarrow \left|A+B\right|=\sqrt{202} \end{gathered}$$

Hence option $\left(D\right)$ is the correct option.