UCL Online STEP and AEA Preparation Sessions
Session 16: Vectors and coordinate geometry
Practising vectors and coordinate geometry questions is very worthwhile. Confidence
can be built quite quickly. A theme of this session will be situations which require
working with general coordinates or vectors rather than with coordinates and vectors
given explicitly. For example
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d),
respectively.
In terms of a, b, c and d, what are the coordinates of the other two vertices?
We’ll look at methods for calculating angles, lengths and ratios of lengths in
questions based on vectors and coordinate geometry.
Careful use of notation can be very helpful when attempting vectors questions.
Example problem
If A is the point (a, 0, 0), B is the point (0, b, 0) and C is the point (0, 0, c) show that
c2
cos( ACB) 
 a2  c2 b2  c2 