10.1.5

Vector Proofs

Test yourself

Proof by Vector Method

Vectors can be used to prove geometric properties of shapes.

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Example

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

  • Remember to label each points carefully.
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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.
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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.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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