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

Answer

A

Explanation

`vec(tau)= vec(r) xx vec(F) = (7 hat(i) + 3hat(j) + hat(k)) (-3hat(i) + hat(j) + 5hat(k))`
`vec(tau)= |(hat(i),hat(j),hat(k)),(7,3,1),(-3,1,5)|= 14 hat(i)- 38 hat(j) + 16hat(k)`