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Vector Proofs

Maths: Edexcel A Level Pure Maths, topic 10.1.5

Proof by Vector Method

Vectors can be used to prove geometric properties of shapes.

Example

Example

  • By method of vectors, prove that STU is a straight line.
Draw the diagram

Draw the diagram

  • Remember to label each points carefully.
Work out the vectors

Work out the vectors

  • Work out the vectors for the points connecting the path from S to T to U, in terms of the vectors p and q.
Work out the vectors

Work out the vectors

Compare

Compare

  • Compare the vector ST with the vector TU.
  • If STU is a straight line, then ST and TU will be multiples of one another with T as a common point.
Compare

Compare

Test yourself on Vector Proofs

  • If AB→=\overrightarrow{AB} = a and BC→=\overrightarrow{BC} = c, and E and F are the midpoints of BC and AC respectively, what is AF→\overrightarrow{AF} equal to?

Practise this topic for free