A rigid body is in equilibrium under the action of three forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 } \mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) act at the points with position vectors \(\mathbf { r } _ { 1 }\) and \(\mathbf { r } _ { 2 }\) respectively, where \(\mathbf { F } _ { 1 } = ( 2 \mathbf { j } + \mathbf { k } ) \mathrm { N } \quad \mathbf { r } _ { 1 } = ( \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } ) \mathrm { m } \mathbf { F } _ { 2 } = ( - 2 \mathbf { i } - \mathbf { j } ) \mathrm { N } \quad \mathbf { r } _ { 2 } = ( - \mathbf { i } - \mathbf { j } + \mathbf { k } ) \mathrm { m }\)
Find the magnitude of \(\mathbf { F } _ { 3 }\)
Find a vector equation of the line of action of \(\mathbf { F } _ { 3 }\), giving your answer in the form \(\mathbf { r } = \mathbf { a } + t \mathbf { b }\), where \(\mathbf { a }\) and \(\mathbf { b }\) are constant vectors and \(t\) is a scalar parameter.