A quadrilateral changes shape with the edge lengths constant. Show
the scalar product of the diagonals is constant. If the diagonals
are perpendicular in one position are they always perpendicular?
The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates. . . .
An account of multiplication of vectors, both scalar products and
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore how matrices can fix vectors and vector directions.
Stick some cubes together to make a cuboid. Find two of the angles
by as many different methods as you can devise.
Form a sequence of vectors by multiplying each vector (using vector
products) by a constant vector to get the next one in the
seuence(like a GP). What happens?
Play countdown with vectors.
This problem in geometry has been solved in no less than EIGHT ways
by a pair of students. How would you solve it? How many of their
solutions can you follow? How are they the same or different?. . . .
Find the distance of the shortest air route at an altitude of 6000
metres between London and Cape Town given the latitudes and
longitudes. A simple application of scalar products of vectors.
As a quadrilateral Q is deformed (keeping the edge lengths constnt)
the diagonals and the angle X between them change. Prove that the
area of Q is proportional to tanX.
A simplified account of special relativity and the twins paradox.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.