Force $$\hat i + 2\hat j - 3\hat k,\,2\hat i + 3\hat j + 4\hat k$$       and $$ - \hat i - \hat j + \hat k$$    are acting at the point $$P\left( {0,\,1,\,2} \right).$$    The moment of these forces about the point $$A\left( {1,\, - 2,\,0} \right)$$    is :

Solution :
If $$\overrightarrow F $$ be the resultant force, then $$\overrightarrow F = 2\hat i + 4\hat j + 2\hat k$$
Also, $$\overrightarrow r = \overrightarrow {AP} = - \hat i + 3\hat j + 2\hat k$$
$$\therefore $$  Required moment
\[ = \overrightarrow r \times \overrightarrow F = \left| \begin{array}{l} \,\,\,\hat i\,\,\,\,\,\,\,\,\hat j\,\,\,\,\,\hat k\\ - 1\,\,\,\,\,3\,\,\,\,\,2\\ \,\,\,2\,\,\,\,\,\,\,4\,\,\,\,\,2 \end{array} \right| = - 2\hat i + 6\hat j - 10\hat k\]