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?. . . .
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. . . .
Play countdown with vectors.
Can you combine vectors to get from one point to another?
The classic vector racing game.
Can you make matrices which will fix one lucky vector and crush another to zero?
An account of multiplication of vectors, both scalar products and vector products.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you work out the fraction of the original triangle that is covered by the green triangle?
Explore the lattice and vector structure of this crystal.
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?
Explore how matrices can fix vectors and vector directions.
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.
Can you find the area of a parallelogram defined by two vectors?
A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
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?
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?
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
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 simulations.