You may also like 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? 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. 8 Methods for Three by One

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? Which do you like best?

Vector Walk

Age 14 to 18 Challenge Level:
Try creating some walks from combinations of $b_1$ and $b_2$. Do you notice anything about the destinations you reach? Can you explain what you find?

What is the simplest horizontal step you can make by combining $b_1$ and $b_2$ steps? What about vertically?

This problem builds on GCSE level vector work, and provides a foundation for concepts met in the later Core A Level modules.