Vectors in problem solvingAQA A-Level Maths: Flashcards

What these 12 flashcards ask

If AM:MB=1:3, what is \overrightarrow{AM} in terms of \overrightarrow{AB}?
How do you find a vector in a geometric figure?
What shows that points P, Q and R are collinear?
When can you equate coefficients of \mathbf a and \mathbf b?
How do you find where two lines meet using vectors?
What is the resultant of a set of forces?
What is the condition for equilibrium?
How do you find an unknown force in equilibrium?
Newton's second law in vector form?
Position of a body with initial position \mathbf r0 and constant velocity \mathbf v after time t?
What does due north mean for a position vector in \mathbf i,\mathbf j form?
Why use a different scalar for each line?

Exam questions on Vectors in problem solving

A particle of mass $2$ kg is acted on by two forces, $\mathbf F_1=(3\mathbf i+2\mathbf j)$ N and $\mathbf F_2=(-5\mathbf i+4\mathbf j)$ N, where $\mathbf i$ and $\mathbf j$ are perpendicular unit vectors.
The force $\mathbf F_3$ is removed, so that only $\mathbf F_1$ and $\mathbf F_2$ act. Find the acceleration of the particle.2 marks
The points $P$ , $Q$ and $R$ have position vectors $\mathbf p=\mathbf i+2\mathbf j$ , $\mathbf q=3\mathbf i+8\mathbf j$ and $\mathbf r=k\mathbf i+14\mathbf j$ , where $k$ is a constant.
Given that $P$ , $Q$ and $R$ are collinear, find the value of $k$ .2 marks
Relative to a port $O$ , the unit vectors $\mathbf i$ and $\mathbf j$ point due east and due north, and distances are in kilometres. At noon a ship is at the point with position vector $(8\mathbf i+6\mathbf j)$ km. It moves with constant velocity $(-2\mathbf i+\mathbf j)$ km h⁻¹.
Find the position vector of the ship at 15:00 and its distance from $O$ at that time.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).