Problem Solving using 3D Vectors (Edexcel International A Level Maths: Pure 4)

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Problem Solving using 3D Vectors

Problem-solving with 3-D vectors

  • 3-D vector problems can be solved using the same principles as 2-D vector problems (see Problem Solving using Vectors)
  • Vectors can be used to prove two lines are parallel, to show points are collinear (lie on the same straight line) or to find missing vertices of a given shape

Problem Solving using 3-D Vectors Diagram 1, AS & A Level Maths revision notes

Using trig in 3-D vector problems

  • 3-D vector problems can also involve using trigonometry to:
    • find the angle between two vectors using Cosine Rule
    • find the area of a triangle using a variation of Area Formula

Problem Solving using 3-D Vectors Diagram 2, AS & A Level Maths revision notes

  • You can find the angle between a vector and any one of the coordinate axes by using the following formulae

 Problem Solving using 3-D Vectors Diagram 3a, AS & A Level Maths revision notes

 

Problem Solving using 3-D Vectors Diagram 3b, AS & A Level Maths revision notes

  • These formulae are not in the exam formulae book
  • However, they may be derived using SOHCAHTOA as shown in the diagram
  • The formulae also work for vectors in two dimensions

Examiner Tip

  • If there is a diagram, labelling all known vectors and quantities will help, and don’t worry about trying to make your diagram 3-D, as long as you label it well.

Worked example

Problem Solving using 3-D Vectors 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.