#### 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.