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

(A) The torque is defined as `tau=vec(r)xxvec(F)`
`vec(r)xxvec(F)=|(hat(i), hat(j) , hat(k)),(7, 3, 1),(-3, 1 , 5)|`
`=hat(i)|(3,1),(1, 5)|+hat(j)|(1, 7),(5, -3)| + hat(k)|(7, 3), (-3, 1)|`
`=hat(i)(15-1)+hat(i)(-3-35)+hat(k)|(7-(-9))`
`=14hat(i)-38hat(j)+16hat(k)`
Thus the answer is (A)