The torque of a force `F = -2 hat(i) +2 hat(j) +3 hat(k)` acting on a point `r = hat(i) - 2 hat(k)+hat(k)` about origin will be

Options

A. `8 hat(i)+5 hat(j)+2 hat(k)`
B. `-8 hat(i)-5hat(j)-2 hat(k)`
C. `8 hat(i)-5 hat(j)+2 hat(k)`
D. `-8 hat(i)+5 hat(j)-2 hat(k)`

Answer

B

Explanation

Torque, `tau = r xx F`
`=|{:(hat(i),hat(j),hat(k)),(1,-2,+1),(-2,2,+3):}|`
`=hat(i)(-6-2)+hat(j)(-2-3)+hat(k)(2-4)]`
Torque of force, `tau=-8 hat(i)-5 hat(j)-2hat(k)`.