Vector Addition (AQA AS Maths: Pure)

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Vector Addition

Vector addition

  • Adding vectors together lets us describes the movement between two points
  • The single vector this creates is called the resultant vector
  • Subtracting a vector is the same as adding the negative vector
  • Adding the vectors PQ and QP gives the zero vector, denoted by a bold zero 0

 

Vector Addition Diagram 1a, AS & A Level Maths revision notes

  • You can add and subtract vectors in any of the forms previously described:

 

Vector Addition Diagram 1b, AS & A Level Maths revision notes

Scalars and parallel vectors

  • Multiplying by a positive scalar only changes the size of a vector, not its direction
  • Two vectors are parallel if and only if one is a scalar multiple of the other

 

Vector Addition Diagram 2, AS & A Level Maths revision notes

Examiner Tip

  • Think of vectors like a journey from one place to another – you may have to take a detour eg. A to B might be A to O then O to B.
  • Diagrams can help, so if there isn’t one, draw one. If there are any, labelling parallel vectors will help.

Worked example

Vector Addition Example Solution, AS & A Level Maths revision notes

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Lucy

Author: Lucy

Expertise: Head of STEM

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.