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The moment of the couple consisting of t...

The moment of the couple consisting of the force through the point `2hati -3hatj -hatk` is

A

5

B

`5sqrt5`

C

`sqrt5`

D

25

Text Solution

Verified by Experts

The correct Answer is:
B
Let A and B be the points having position vectors
` hati - hatj + hatk and 2hati -3hatj -hatk` respectively, then
`vecr = vec(BA) = (hati -hatj +hatk) - ( 2hati -3hatj -hatk) = - hati + 2hatj + 2hatk`
Let `vecM` b the moment of the couple. Then,
` vecM = vecr xx vecF |{:(hati, hatj ,hatk),(-1,2,2),( 3,2,-1):}| = -6 hati +5hatj -8hatk`
Moment fo the couple = ` |vecM|= sqrt(36+25+ 64) = 5sqrt5`
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