Find the workdone if a particle moves from position `vec(r )_(1)=(2hat(j)+hat(j)-3hat(k))` to a position `vec(r )_(2)=(4hat(i)+6hat(j)-7hat(k))` under the effect of force `vec(F)=(3hat(i)+2hat(j)+4hat(k))N`.

Explanation

`vec(r )_(1)=(2hat(i)+hat(j)-3hat(k))`
`vec(r )_(2)=(4hat(i)+6hat(j)-7hat(k))`
The position vectors `vec(r )= vec(r )_(2)-vec(r )_(1)`
`= (4hat(i)+6hat(j)-7hat(k))-(2hat(i)+hat(j)-3hat(k))=4hat(i)+6hat(j)-7hat(k)-2hat(i)-hat(j)+3hat(k)`
`= hat(i)(4-2)+hat(j)(6-1)+hat(k)(-7+3)=hat(i)(2)+hat(j)(5)+hat(j)(5)+hat(k)(-4)`
`vec(r ) = vec(r )_(2)-vec(r )_(1)=2hat(i)+5hat(j)-4hat(k)`
The effect of force `vec(F )=(3hat(i)+2hat(j)+2hat(j)+4hat(k))N`
Workdone `W = vec(F ).vec(x)`
`= (3hat(i)+2hat(j)+4hat(k)).(2hat(i)+5hat(j)-4hat(k))=hat(i).hat(j).hat(k)(6+10-16)=1(0)`
Work done = 0.