Edexcel IGCSE Maths 复习笔记 5.1.2 Vectors - Finding Paths

Edexcel IGCSE Maths 复习笔记 5.1.2 Vectors - Finding Paths

Finding paths in vector diagrams

  • It is important to be able to describe vectors by following paths through a geometric diagram
  • The following grid is made up entirely of parallelograms, with the vectors  and  defined as marked in the diagram:

 

Vector-parallelogram-grid

 

7.19.2-Vectors-Finding-Paths-RN-1Vector-paths-vector-FB-01

 

  • Getting from point to point  we have to go the 'wrong way' down  and then the 'right way' along

Vector-paths-vector-FB-02

 

 

  • It follows that:

7.19.2-Vectors-Finding-Paths-RN-2

  • Keeping those things in mind, it is possible to describe any vector that goes from one point to another in the above diagram in terms of a and b

 

Exam Tip

Adding and subtracting vectors follows all the same rules as adding and subtracting letters like x and y in algebra (this includes collecting like terms).It doesn't matter exactly what path you follow through a diagram from starting point to ending point – as long as you add and subtract the general vectors correctly along the path you use, you will get the correct answer.

Worked Example

7.19.2-Vectors-Finding-Paths-Worked-Example-1Vector-parallelogram-grid

Worked Example

7.19.2-Vectors-Finding-Paths-Worked-Example-2

转载自savemyexam

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