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