The moment of the force `vecF = 4 hati + 5hatj - 6hatk` at (2 , 0 , -3) , about the point (2 , -2 ,-2) , is given by

Options

A. `- 8 hati - 4hatj - 7hatk`
B. `-4hati - hatj - 8hatk`
C. `-7hati - 8 hatj - 4hatk`
D. `-7hati - 4hatj - 8hatk`

Answer

D

Explanation

Moment of the force is , `vectau = (vecr - vecr_(0)) xx vecF`
Here , `vecr_(0) = 2 hati - 2hatj - 2hatk` and `vecr = 2 hati + 0 hatj - 3hatk`
`therefore vecr - vecr_(0) = (2 hati +0 hatj - 3hatk) - (2hati - 2hatj - 2hatk) = 0 hati + 2hatj - hatk`
`therefore tau = |{:(hati , hatj , hatk) , (0 , 2 , -1) , (4 , 5 , -6):}| = -7hati - 4hatj - 8hatk`