Question

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

• A. $10$
• B. $5$
• C. $6$
• D. $3$

Answer 1

Answer: (B)

Given, $\overset{ \rightarrow }{A}=7\hat{i}+6\hat{j}$
Let $\overset{ \rightarrow }{B}=b_{1}\hat{i}+b_{2}\hat{j}$ ......(i)
Given that, $\overset{ \rightarrow }{A}+\overset{ \rightarrow }{B}=11\hat{i}+9\hat{j}$
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),
$\overset{ \rightarrow }{B}=4\hat{i}+3\hat{j}$
$\left|\overset{ \rightarrow }{B}\right|=\sqrt{4^{2} + 3^{2}}=\sqrt{25}=5$