Question

Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously $\overrightarrow{F_1}=-4\hat{i}-5\hat{j}+5\hat{k},\overrightarrow{F_2}=-5\hat{i}+8\hat{j}+6\hat{k},\overrightarrow{F_3}=-3\hat{i}+4\hat{j}-7\hat{k}$ and $\overrightarrow{F_4}=12\hat{i}-3\hat{j}-2\hat{k}$ then the particle will move

• A. in $x-y$ plane
• B. in $y-z$ plane
• C. in $x-z$ plane
• D. along x-axis

Answer 1

The correct option is B in $y-z$ plane

$\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}+\overrightarrow{F_4}=\left(\begin{array}{c}-4\hat{i}-5\hat{j}+5\hat{k}\end{array}\right)+\left(\begin{array}{c}-5\hat{i}+8\hat{j}+6\hat{k}\end{array}\right)+\left(\begin{array}{c}-3\hat{i}+4\hat{j}-7\hat{k}\end{array}\right)+\left(\begin{array}{c}12\hat{i}-3\hat{j}-2\hat{k}\end{array}\right)$

$=4\hat{j}+2\hat{k}$

$\Rightarrow$ motion will be in y-z plane