Vectors in problem solvingEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

How do you find the fourth vertex D of parallelogram ABCD?
What do the diagonals of a parallelogram do?
If AP:PB=1:2, what fraction of AB is AP?
How do you prove three points are collinear?
What is the resultant of several forces?
What is the resultant when a particle is in equilibrium?
How do you find a force needed for equilibrium?
Give the position of a body with constant velocity \mathbf{v} from \mathbf{r}0.
What is speed in terms of velocity?
What does 'due east of O' mean in components?
How can you tell if a parallelogram is a rectangle?
How is the direction of a force a\mathbf{i}+b\mathbf{j} found?

Exam questions on Vectors in problem solving

Relative to an origin $O$ , the points $A$ , $B$ and $C$ have position vectors $\mathbf{a}=\mathbf{i}+2\mathbf{j}$ , $\mathbf{b}=5\mathbf{i}+3\mathbf{j}$ and $\mathbf{c}=8\mathbf{i}+7\mathbf{j}$ . The quadrilateral $ABCD$ is a parallelogram.
Find the position vector of the point where the diagonals $AC$ and $BD$ meet.2 marks
Two forces $\mathbf{F}_1=(5\mathbf{i}+2\mathbf{j})$ N and $\mathbf{F}_2=(-3\mathbf{i}+7\mathbf{j})$ N act on a particle, where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors due east and due north. A third force $\mathbf{F}_3$ also acts, and the particle is in equilibrium.
Find the angle that the resultant of $\mathbf{F}_1$ and $\mathbf{F}_2$ makes with the direction of $\mathbf{i}$ , giving your answer to 1 decimal place.2 marks
At time $t=0$ a ship leaves a point with position vector $(2\mathbf{i}-5\mathbf{j})$ km relative to a port $O$ , and then moves with constant velocity $(3\mathbf{i}+4\mathbf{j})$ km h $^{-1}$ , where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors due east and due north.
Find the speed of the ship and its position vector after $t$ hours.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).