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
Spiroflowers

Age

16 to 18

Challenge level

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
problem
Areas of parallelograms

Age

14 to 16

Challenge level

Can you find the area of a parallelogram defined by two vectors?
problem
Triangle in a triangle

Age

14 to 16

Challenge level

Can you work out the fraction of the original triangle that is covered by the inner triangle?
problem
Tetra perp

Age

16 to 18

Challenge level

Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.
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
Flexi quads

Age

16 to 18

Challenge level

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?
article
Multiplication of vectors

An account of multiplication of vectors, both scalar products and vector products.
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
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.