Problem Solving using 3D Vectors (Cambridge International A-Level Mathematics)

Problem solving using 3D vectors

How are 3D vectors used for problem solving?

• 3D vector problems can be solved using the same principles as 2D 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

When do I use trigonometry in 3D vector problems?

• 3D 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

• 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 Hint

• 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