Vectors and resultantsEdexcel International A Level Maths: Mind map

Exam questions on Vectors and resultants

1. Two forces act on a particle: $\mathbf{F}_1=(7\mathbf{i}-3\mathbf{j})$ N and $\mathbf{F}_2=(-2\mathbf{i}+6\mathbf{j})$ N, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in the horizontal plane, in the directions east and north.
   Find the angle between the resultant force and the direction east, giving your answer in degrees to 1 decimal place.2 marks
2. A force $\mathbf{F}$ of magnitude 24 N acts on a particle in a direction $40^\circ$ above the direction of the unit vector $\mathbf{i}$, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in a vertical plane, horizontal and vertically upwards respectively.
   A second force $\mathbf{G}=(-10\mathbf{i}-6\mathbf{j})$ N also acts on the particle. Find the magnitude of the resultant of $\mathbf{F}$ and $\mathbf{G}$.2 marks
3. Three forces $\mathbf{P}=(3\mathbf{i}+5\mathbf{j})$ N, $\mathbf{Q}=(-7\mathbf{i}+2\mathbf{j})$ N and $\mathbf{R}=(p\mathbf{i}+q\mathbf{j})$ N act on a particle, where $p$ and $q$ are constants. The particle is in equilibrium.
   Find the values of $p$ and $q$.3 marks