A particle, which remains at rest, is acted on by three forces, P, Q and R, and no others, as shown in the diagram attached. The force P acts horizontally to the left, the force Q acts vertically upwards and the force R acts downwards and to the right at an angle of 30◦ to the horizontal. The magnitude of P is 52 N. Let the magnitudes of Q and R in newtons be Q and R respectively. Take the Cartesian unit vectors i and j to be in the opposite direction to P and in the same direction as Q, respectively.   a) Find expressions for the component forms of the three forces P, Q and R. b) Hence or otherwise find Q to two significant figures.

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