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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?

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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.

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Air Routes

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Coordinated Crystals

Stage: 5 Challenge Level: Challenge Level:1
Focus on the atom at the origin and its nearest neighbours to begin with.

Use the scalar product to work out the angles once you have visualised the structure.