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A force of magnitude 4 unit acting along...

A force of magnitude 4 unit acting along the vector `2hati-2hatj+hatk` displaces the point of applications from (1,2,3) to (5,3,7), then the work done is

A

50/7 unit

B

40/3 unit

C

25/3 unit

D

25/4 unit

Text Solution

Verified by Experts

The correct Answer is:
B
Given force `=4((2hati-2hatj+hatk)/(|2hati-2hatj+hatk|))`
`=(4)/(3)(2hati-2hatj+hatk)`
Displacement `=(5hati+3hatj+7hatk)-(hati+2hatj+3hatk)`
`=4hati+hatj+4hatk`
`therefore` Required work done=force displacement
`=(4)/(3)(2hati-2hatj+hatk)*(4hati+hatj+4hatk)`
`=(40)/(3)` unit
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