Problem Solving using 3D Vectors (Edexcel A Level Maths): Revision Note

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

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

• 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