The torque of force `vec(F)=-3hat(i)+hat(j)+5hat(k)` acting at the point `vec(r)=7hat(i)+3hat(j)+hat(k)` is ______________?

Options

A. `14hat(i)-38hat(j)+16hat(k)`
B. `4hat(i)+4hat(j)+6hat(k)`
C. `21hat(i)+4hat(j)+4hat(k)`
D. `-14hat(i)+34hat(j)-16hat(k)`

Answer

A

Explanation

`vec(tau)=vec(r)xxvec(F)=(7hat(i)+3hat(j)+hat(k))(-3hat(i)+hat(j)+5hat(k))`
`vectau=|{:(hati,hatj,hatk),(7,3,1),(-3,1,5):}|=14hati-38hatj+16hatk`