AQA A Level Maths: Pure复习笔记11.2.2 Problem Solving using 3D Vectors

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


  • You can find the angle between a vector and any one of the coordinate axes by using the following formulae 11.2.2-Problem-Solving-using-3-D-Vectors-Diagram-3a


  • 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

Exam 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