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If the constant forces 2hati-5hatj+6hatk...

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

Text Solution

Verified by Experts

The correct Answer is:
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"`
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