Q. A vector $\overrightarrow{A}$ when added to the vector $\overrightarrow{B}$ =$3\widehat{i} + 4\widehat{j}$ 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) $\sqrt{15}$
Explanation
(a) Given $\overrightarrow{C} = \left| \overrightarrow{B}\ \right|\widehat{j}\ \ \ \Rightarrow \ \ \ \overrightarrow{C} = 5\widehat{j}$
Let $\overrightarrow{C} = \overrightarrow{A} + \overrightarrow{B} = A + 3\widehat{i} + 4\widehat{j}$
$5\widehat{j} = A + 3\widehat{i} + 4\widehat{j}$
$\mathbf{\Rightarrow \ \ }\overrightarrow{A} =$-$3\widehat{i} + \widehat{j}$
$\left| \overrightarrow{A}\ \right| = \sqrt{(3)^{2} + (1)^{2}}$
$\mathbf{=}\sqrt{10}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.