Question

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

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

Answer 1

Answer: (D)

Given, $\vec{A}=\hat{6}+7\hat{j}+0\hat{k}$ and $\vec{B}=3\hat{i}+4\hat{j}+0\hat{k}$ Sum of two vectors $=\vec{A}+\vec{B}$ $=(6\hat{i}+7\hat{j}+0\hat{k})+(3\hat{i}+4\hat{j}+0\hat{k})$ $=(6+3)\hat{i}+(7+4)\hat{j}+(0+0)\hat{k}$ $=9\hat{i}+11\hat{j}$ Therefore, magnitude of the sum of twovectors $=\sqrt{{(9)}^2+{(11)}^2}$ $=\sqrt{81+121}$ $=\sqrt{202}$