AQA A Level Maths: Pure复习笔记11.1.5 Problem Solving using Vectors

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


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)


Exam 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