The moment of the force, \(\overrightarrow {\;F} = 4\hat i + 5\hat j - 6\hat k\) at \((2, 0, -3),\) about the point \((2, -2, -2),\) is given by

Moment of the force is, \(\begin{array}{l}
\overrightarrow \tau   = \left( {\overrightarrow r  - \overrightarrow {{r_0}} } \right) \times \overrightarrow F \\
Here,\,\overrightarrow {{r_0}}  = 2\hat i - 2\hat j - 2\hat k\\
and\,\,\overrightarrow r  = 2\hat i + 0\hat j - 3\hat k\\
\therefore \,\overrightarrow r  - \overrightarrow {{r_0}}  = \left( {2\hat i + 0\hat j - 3\hat k} \right) - \left( {2\hat i - 2\hat j - 2\hat k} \right)\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0\hat i + 2\hat j - \hat k\\
\therefore \,\,\,\overrightarrow \tau  \, = \left| \begin{array}{l}
\hat i\,\,\,\,\,\,\hat j\,\,\,\,\,\,\,\,\hat k\\
0\,\,\,\,\,\,2\,\,\,\,\, - 1\\
4\,\,\,\,\,\,5\,\,\,\, - 6
\end{array} \right| =  - 7\hat i - 4\hat j - 8\hat k
\end{array}\)