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 $B$ . Find the magnitude of $\overrightarrow{A}$.

• A. $\sqrt{10}$
• B. $6$
• C. $5$
• D. $10$

Answer 1

Answer: (A)

$\sqrt{10}$

Let $A=x\hat{i}+y\hat{j}$

Resultant, $C=A+B=(x+3)\hat{i}+(y+4)\hat{j}$

but $C$ is in $+Y$ direction.

$⟹x+3=0$

$⟹x=-3$ ............... (1)

since, $|C|=|B|$

$|(y+4)\hat{j}|=|3\hat{i}+4\hat{j}|$

$y+4=\sqrt{(3^2+4^2)}$

$y+4=5$

$⟹y=1$ ......... (2)

Now, from equation (1) and (2)

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

$|A|=\sqrt{\left(\right(-3{)}^2+1^2)}=\sqrt{(9+1)}=\sqrt{10}$