The moment of the couple formed by the forces $5\hat i+\hat k$ and $-5\hat i - \hat k$ acting at the points (9, –1, 2) and (3, –2, 1) respectively, is:

$\hat i-\hat j-5\hat k$

Moment = $\vec r×\vec F=[(9\hat i-\hat j+2\hat k)-(3\hat i-2\hat j+\hat k)]×(5\hat i+\hat k)$

$=[6\hat i+\hat j +\hat k]×(5\hat i+\hat k)=\begin{vmatrix}\hat i&\hat j&\hat k\\6&1&1\\5&0&1\end{vmatrix}=\hat i-\hat j-5\hat k$