You may also like

Flexi Quads

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?

Flexi Quad Tan

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

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.

Fix Me or Crush Me

Age 16 to 18 Challenge Level:

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.