Question

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ of magnitude 2 units and 1 unit, respectively are directed along the x-axis and y-axis. Their resultant $\overrightarrow{A}+\overrightarrow{B}$ is directed along the line:

• A. $y-2x=0$
• B. $2y-x=0$
• C. $y+x=0$
• D. $y-x=0$

Answer 1

The correct option is B $2y-x=0$

Resultant of $\overrightarrow{A}\&\overrightarrow{B}$ made an angle of $\tan \theta =\frac{1}{2}or\theta ={\tan }^{-1}\left(\frac{1}{2}\right)$ with x-axis.
Slope of resultant line $m=\tan \theta =\frac{1}{2}$ and it passes through origin.
Using: $y=mx$ which gives $y=\frac{1}{2}xor2y=xor2y-x=0$