Question

The magnitude of $x$ and $y$ components of $\overrightarrow{A}$ are $7$ and $6$ respectively. Also, the magnitudes of $x$ and $y$ components of $\overrightarrow{A}+\overrightarrow{B}$ are $11$ and $9$ respectively. Calculate the magnitude of vector $\overrightarrow{B}$ .

• A. $10$
• B. $5$
• C. $6$
• D. $3$

Answer 1

Answer: (B)

Given, $\overrightarrow{A}=7\hat{i}+6\hat{j}$
Let $\overrightarrow{B}=b_1\hat{i}+b_2\hat{j}$ ......(i)
Given that, $\overrightarrow{A}+\overrightarrow{B}=11\hat{i}+9\hat{j}$
Or $\left(7+b_1\right)\hat{i}+\left(6+b_2\right)\hat{j}=11\hat{i}+9\hat{j}$
Comparing the scalar component of $\hat{i}$ and $\hat{j}$
$7+b_1=11$ and $6+b_2=9$
$\Rightarrow b_1=4$ and $b_2=3$
$\therefore$ From Equation. (i),
$\overrightarrow{B}=4\hat{i}+3\hat{j}$
$\left|\overrightarrow{B}\right|=\sqrt{4^2+3^2}=\sqrt{25}=5$