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?

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

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. . . .

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

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?

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?

Can you find the area of a parallelogram defined by two vectors?

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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