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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?

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.

Multiplication of Vectors

An account of multiplication of vectors, both scalar products and vector products.

Air Routes

Age 16 to 18 Challenge Level:
Find vectors $\overline{OL}$ and $\overline{OC}$ and use the scalar product.