# Question on Finding Torque Using Cross Product

Let r equal the line segment OP=i-j+2k. A force F=<10,10,0> is applied at P. Find the torque O produced.

In calculus we learned that torque is equal to the cross product of the force vector and the radius (arm). However I am having the feeling that in this situation, the answer may not be as simple.

Can anyone confirm or refute?

Yes, by definition $\vec{\tau} = \vec{r} \times \vec{F}$
Assuming $i,j,k$ are the unity vectors specifying the Cartesian coordinates, then:
$$\vec{r} \times \vec{F} = \begin{vmatrix} i && j && k \\ 1 && -1 && 2 \\ F_x && F_y && F_z \\ \end{vmatrix} = \begin{vmatrix} i && j && k \\ 1 && -1 && 2 \\ 10 && 10 && 0 \\ \end{vmatrix} = (-20,20,20)$$