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CIE A Level Maths: Pure 3復(fù)習(xí)筆記7.1.5 Problem Solving using Vectors

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月19日 下午5:56

Problem Solving using Vectors

Problem-solving with vectors

  • Vectors can be used to prove two lines are?parallel?(see Vector Addition)
  • They can also be used to show points are?collinear?(lie on the same straight line)
  • Vectors can be used to find missing vertices of a given shape
  • You will need a good understanding of how to divide a line segment into a given ratio

11.1.5-Problem-Solving-using-Vectors-Diagram-1a

11.1.5-Problem-Solving-using-Vectors-Diagram-1b

Using trig in vector problems

  • When problem-solving with vectors, trigonometry can help us:
    • convert between?component form?and magnitude/direction form (see Magnitude Direction)
    • find the?angle between two vectors?using?Cosine Rule?(see Non-Right-Angled Triangles)
    • find the?area of a triangle?using a variation of?Area Formula?(see Non-Right-Angled Triangles)

11.1.5-Problem-Solving-using-Vectors-Diagram-2

Exam Tip

  • Think of vectors like a journey from one place to another – you may have to take a detour eg. A to B might be A to O then O to B.
  • Diagrams can help, if there isn’t one, draw one. For a given diagram labelling all known vectors and quantities will help.

Worked Example

11.1.5-Problem-Solving-using-Vectors-Example-Solution

 

 

 

 

 

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