What is the torque of a force `3hati+7hatj+4hatk` about the origin, if the force acts on a particle whose position vector is

Options

A. `hati - 5hatj + 8 hatk`
B. `2hati + 2hatj + 2hatk`
C. `hati + hatj + hatk`
D. `3hati + 2hatj + 3hatk`

Answer

A

Explanation

Here , `vecr = 2 hati + 2hatj + 1 hatk , vecF = 3 hati + 7 hatj + 4hatk`
Torque , `vectau = vecr xx vecF`
`r = |{:(hati , hatj , hatk) , (2 , 2 , 1) , (3 , 7 , 4):}| = hati(8-7) - hatj (8-3) + hatk (14 - 6) = hati - 5hatj + 8hatk`