Question

If the constant forces `2hati-5hatj+6hatk and -hati+2hatj-hatk` act on a particle due to which it is displaced from a point A (4,-3,-2) to a point B (6,1,-3), then the work done by the forces is
A. 15 unit
B. 9 unit
C. `-15 "unit"`
D. `-9 "unit"`

Answer 1

Correct Answer - C
Resultant force, `vecF=(2hati-5hatj+6hatk)+(-hati+2hatj-hatk)=hati-3hatj+5hatjk`
Displacement,
`vecd=vec(AB)=(6hati+hatj-3hatk)-(4hati-3hatj-2hatk)`
`=2hati+4hatj-hatk`
`W=vecF.vecd=(hati-3hatj+5hatk).(2hati+4hatj-4hatk)`
`=2-12=5=-15"unit"`