3. Three forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) act on a rigid body at the points with position vectors \(\mathbf { r } _ { 1 } , \mathbf { r } _ { 2 }\) and \(\mathbf { r } _ { 3 }\) respectively.
\(\mathbf { F } _ { 1 } = ( 2 \mathbf { i } + 3 \mathbf { j } - \mathbf { k } ) \mathrm { N }\) and \(\mathbf { r } _ { 1 } = ( \mathbf { i } + \mathbf { j } - 2 \mathbf { k } ) \mathrm { m }\),
\(\mathbf { F } _ { 2 } = ( \mathbf { i } - 4 \mathbf { j } - 2 \mathbf { k } ) \mathrm { N }\) and \(\mathbf { r } _ { 2 } = ( 3 \mathbf { i } - \mathbf { j } - \mathbf { k } ) \mathrm { m }\),
\(\mathbf { F } _ { 3 } = ( - 3 \mathbf { i } + \mathbf { j } + 3 \mathbf { k } ) \mathrm { N }\) and \(\mathbf { r } _ { 3 } = ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } ) \mathrm { m }\).
Show that the system is equivalent to a couple and find the magnitude of the vector moment of this couple.