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A LevelMaths: PureAQARevision Notes11. Vectors11.1 Vectors in 2 Dimensions11.1.5 Problem Solving using Vectors

Problem Solving using Vectors (AQA A Level Maths: Pure)

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Problem Solving using Vectors

Problem-solving with vectors

  • Vectors can be used to prove two lines are parallel (see Vector Addition)
  • They can also be used to show points are collinear (lie on the same straight line)
  • Vectors can be used to find missing vertices of a given shape
  • You will need a good understanding of how to divide a line segment into a given ratio

Problem Solving using Vectors Diagram 1a, AS & A Level Maths revision notes

Problem Solving using Vectors Diagram 1b, AS & A Level Maths revision notes

Using trig in vector problems

  • When problem-solving with vectors, trigonometry can help us:
    • convert between component form and magnitude/direction form (see Magnitude Direction)
    • find the angle between two vectors using Cosine Rule (see Non-Right-Angled Triangles)
    • find the area of a triangle using a variation of Area Formula (see Non-Right-Angled Triangles)

Problem Solving using Vectors 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, if there isn’t one, draw one. For a given diagram labelling all known vectors and quantities will help.

Worked example

new-11-1-5-problem-solving-using-vectors-example-solution

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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.