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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?

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

##### Stage: 5 Challenge Level:
Find vectors $\overline{OL}$ and $\overline{OC}$ and use the scalar product.