A particle is acted upon by following forces:
(i) `2hat(i)+3hat(j)+hat(k) , (ii) -5hat(i)+4hat(j)-3hat(k) and (iii) 3hat(i)-7hat(k)`
In which plane does it move?

Options

A. `x-y` plane
B. `y-z` plane
C. `z-x` plane
D. any arbitrary plane

Answer

B

Explanation

There forces are given by, say, `F_(1), F_(2) and F_(3)`
`vec(F)_(1)= 2 hat(i) + 3 hat(j) + 5 hat(k), vec(F)_(2)=-5hat(i)+4hat(j)+4hat(j)-3hat(k)`
`and vec(F)_(3)=3hat(i)-7hat(k)`
Total resultant force, `vec(F)` is given by
`vec(F)=vec(F)_(1)+vec(F)_(2)+vec(F)_(3)`
`=2hat(i)+3hat(j)+5hat(k)-5hat(i)+4hat(j)-3hat(k)+3hat(i)-7hat(k)=7hat(j)-5hat(k)`
This show that the resultant force is in the y-z plane.
Thus, it moves in the y-z plane.