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The moment of the couple formed by force...

The moment of the couple formed by forces `5hati+hatk and -5hati-hatk` acting at the points (9,-1,2) and (3,-2,1) respectively is,

A

`-hati +hatj +5hatk`

B

` hati -11 hatj -5hatk`

C

` -hati =11hatj +5hatk`

D

` hati -hatj -5hatk`

Text Solution

Verified by Experts

The correct Answer is:
D
we have,
Moment of the couple = `(vecr_(1) -vecr_(2)) xx vecF`
Where ` vecr _(1) and vecr_(2)` are the position vectors of the points of application of the forces ` vecF = 5hati +hatk and -vecF =- 5hati -hatk` respectively.
Hence ` vecr_(1) -vecr_(2) = ( 9hati -hatj +2hatk) - ( 3hati -2hatj +2hatk) = 6hati +hatj +hatk`
and ` vec F = 5 hati + hatk`
Moment of the couple = ` (vecr_(1) -vecr_(2)) xx vecF`
moment of the couple = ` ( 6hati +hatj +hatk)` xx ( 5hati +hatk) = hati -hatj - 5hatk`
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