Question

The force F = i + 3j + 2k acts at the point (1, 1, 1). (a) Find the torque of the force about the point (2, −1, 5). Careful! The vector r goes from (2, −1, 5) to (1, 1, 1)

Answer 1

$$\vec r=(1-2)i+(1-(-1))j+(1-5)k\\ =-i+2j-4k$$

The torque

$$\vec \tau=\vec r\times \vec F=\begin{vmatrix} i & j & k \\ x & y & z\\ F_x & F_y & F_z \end{vmatrix}$$

$$=\begin{vmatrix} i & j & k \\ -1 & 2 & -4\\ 1 & 3 & 2 \end{vmatrix}=16i-2j-5k$$