Torque about a point given coordinates in three dimensions

1. The problem statement, all variables and given/known data



Let [itex]\vec{F}=2\hat{i}-3\hat{j}[/itex] act on an object at point (5,1,3). Find the torque about the point (4,1,0)



2. Relevant equations



[itex]\tau = \vec F \times \vec r[/itex]



3. The attempt at a solution



Please tell me if my procedure is correct.



Let the object occupy point A at (5,1,3) and let (4,1,0) be point B.

Subtracting the distances in each dimension from point A to point B, we see that [itex]\vec{r}=-\hat{i}-3\hat{k}[/itex]



Because [itex]\tau=\vec{F}\times\vec{r}[/itex]:

[tex]\tau = \left[ {\begin{array}{*{20}{c}}

2\\

{ - 3}\\

1

\end{array}} \right] \times \left[ {\begin{array}{*{20}{c}}

{ - 1}\\

0\\

{ - 3}

\end{array}} \right] = 6\hat i + 5\hat j - \hat k[/tex]