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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?

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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?

V-P Cycles

Age 16 to 18 Challenge Level:

The first part of the question focusses on the magnitude of a vector product and simply requires you to show that the magnitudes of the vectors in the sequence are decreasing. The second part focusses on the fact that the vector arising from a vector product is perpendicular to the two vectors and so the sequence of vectors will cycle through perpendicular directions.