Year 11 - Maths
Geometric proofs with vectors
Vectors
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupil understanding of vectors is deepened with pupils exploring column vector notation and arithmetic procedures.
Lesson Summary
You will learn to produce geometric proofs to prove that points are collinear or that vectors are parallel.
Key Notes
- Your knowledge of the properties of polygons can be applied to vector problems.
- A regular polygon has a relationship between sides that can be represented with vector notation.
- Your knowledge can be used to identify vectors and multiples of known vectors.
- Through manipulation, you can prove certain properties.
Vocabulary To Learn
- Collinear: When three or more points lie on a single straight line, these points are said to be collinear.
Common Mistakes To Avoid
- When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Your knowledge of the properties of polygons can be applied to vector problems. A regular polygon has a relationship between sides that can be represented with vector notation.
2. Use this key word in a maths sentence and explain it clearly. 'Collinear'
When three or more points lie on a single straight line, these points are said to be collinear. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors. Correction: Encourage pupils to write a clear vector pathway, sometimes using highlighters can help visualise this pathway.
More Lessons In This Unit
- Addition with vectors Study Guide
- Advanced problem solving with vectors Study Guide
- Algebraic vector notation Study Guide
- Calculating the magnitude of a vector Study Guide
- Checking and securing understanding of translations Study Guide
- Column vectors Study Guide
- Dividing vectors into ratios Study Guide
- Fluency in arithmetic procedures with algebraic vector notation Study Guide
- Fluency in arithmetic procedures with vectors Study Guide
- Multiplication with vectors Study Guide
- Parallel vectors Study Guide
- Parallel vectors in algebraic vector notation Study Guide
- Problem solving with vectors Study Guide
- Subtraction with vectors Study Guide
- The sum and difference with algebraic vector notation Study Guide
Browse all guides in the Year 11 Maths guide library.