A force $$\overrightarrow F = 3\hat i + 4\hat j - 3\hat k$$    is applied at the point $$P,$$ whose position vector is $$\overrightarrow r = 2\hat i - 2\hat j - 3\hat k.$$    What is the magnitude of the moment of the force about the origin ?

Solution :
Moment of force, $$m = \overrightarrow r \times \overrightarrow F $$
\[m = \left| \begin{array}{l} \hat i\,\,\,\,\,\,\hat j\,\,\,\,\,\,\hat k\\ 2\,\,\, - 2\,\,\, - 3\\ 3\,\,\,\,\,\,4\,\,\,\, - 3 \end{array} \right|\]
$$\eqalign{ & = \hat i\left( {6 + 12} \right) - \hat j\left( { - 6 + 9} \right) + \hat k\left( {8 + 6} \right) \cr & = 18\hat i - 3\hat j + 14\hat k \cr & = \sqrt {{{\left( {18} \right)}^2} + {{\left( { - 3} \right)}^2} + {{\left( {14} \right)}^2}} \cr & = \sqrt {529} \cr & = 23{\text{ units}} \cr} $$