| Exam Board | Edexcel |
| Module | M5 (Mechanics 5) |
| Year | 2018 |
| Session | June |
| Topic | Moments |
2. Three forces \(\mathbf { F } _ { 1 } = ( a \mathbf { i } + b \mathbf { j } - 2 \mathbf { k } ) \mathrm { N } , \mathbf { F } _ { 2 } = ( - \mathbf { i } + \mathbf { j } - 2 \mathbf { k } ) \mathrm { N }\) and \(\mathbf { F } _ { 3 } = ( - \mathbf { i } - 3 \mathbf { j } + \mathbf { k } ) \mathrm { N }\), where \(a\) and \(b\) are constants, act on a rigid body.
The force \(\mathbf { F } _ { 1 }\) acts through the point with position vector \(\mathbf { k } \mathrm { m }\), the force \(\mathbf { F } _ { 2 }\) acts through the point with position vector \(( 3 \mathbf { i } - \mathbf { j } + \mathbf { k } ) \mathrm { m }\) and the force \(\mathbf { F } _ { 3 }\) acts through the point with position vector \(( \mathbf { j } + 2 \mathbf { k } ) \mathrm { m }\).
The system of three forces is equivalent to a single force \(\mathbf { R }\) acting through the origin together with a couple of moment \(\mathbf { G }\). The direction of \(\mathbf { R }\) is parallel to the direction of \(\mathbf { G }\).
Find the value of \(a\) and the value of \(b\).