Vector notation and geometry

problem

Quaternions and Rotations

Age

16 to 18

Challenge level

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.
problem

From Point to Point

Age

14 to 16

Challenge level

Can you combine vectors to get from one point to another?
problem

Napoleon's Theorem

Age

14 to 18

Challenge level

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
problem

Hold Still Please

Age

16 to 18

Challenge level

Can you arrange a set of charged particles so that none of them start to move when released from rest?
problem

Coordinated Crystals

Age

16 to 18

Challenge level

Explore the lattice and vector structure of this crystal.
problem

Polygon Walk

Age

16 to 18

Challenge level

Go on a vector walk and determine which points on the walk are closest to the origin.
problem

Matrix Meaning

Age

16 to 18

Challenge level

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
article
An Introduction to Vectors

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 why they are useful.
article
Multiplication of Vectors

An account of multiplication of vectors, both scalar products and vector products.
article
A Knight's Journey

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.