OCR Mechanics 1 2018 March — Question 7

Exam BoardOCR
ModuleMechanics 1 (Mechanics 1)
Year2018
SessionMarch
TopicNewton's laws and connected particles

7 Three forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) acting on a particle are given by $$\mathbf { F } _ { 1 } = ( 3 \mathbf { i } - 2 a \mathbf { j } ) \mathrm { N } , \quad \mathbf { F } _ { 2 } = ( 2 b \mathbf { i } + 3 a \mathbf { j } ) \mathrm { N } \quad \text { and } \quad \mathbf { F } _ { 3 } = ( - 2 \mathbf { i } + b \mathbf { j } ) \mathrm { N } .$$ The particle is in equilibrium under the action of these three forces.
Find the value of \(a\) and the value of \(b\).