Question

A vector $\overrightarrow{A}$ when added to the vector $\overrightarrow{B}=3\hat{i}+4\hat{j}$ yields a resultant vector that is in the positive y-direction and has a magnitude equal to that of $\overrightarrow{B}$. Find the magnitude of $\overrightarrow{A}$.

• A. $\sqrt{10}$
• B. $10$
• C. $5$
• D. $\sqrt{15}$

Answer 1

Answer: (A)

$\sqrt{10}$

As it is said that it is in $y$ axis magnitude of $z$ is equal to magnitude of $B$

$\overrightarrow{B}=3\hat{i}+4\hat{j}$

$|B|=\sqrt{3^2+4^2}=5$

$|B|=5$

Direction of resultant vector Along Y- direction

$\overrightarrow{C}=5\hat{j}$

$\Rightarrow \overline{A}+\overline{B}=\overrightarrow{C}=5\hat{j}$

$\overrightarrow{A}+3\hat{i}+4\hat{j}=5\hat{j}$

$\overrightarrow{A}=\hat{j}-3\hat{i}$

$|A|=\sqrt{3^2+1^2}$

$=\sqrt{10}$