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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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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.

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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?

Fix Me or Crush Me

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This question becomes much more meaningful and straightforward if you consider the geometrical interpretation of the action of a matrix on a vector.

For example, a rotation matrix will leave a line of points invariant.

A matrix which crushes a vector is a type of 'projection'. Clearly a projection must send a non-zero vector to the origin.

This problem uses mathematical concepts found in the later Further Pure Mathematics A Level modules.