Year 11 - Maths
Multiplication 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 multiply with vectors.
Key Notes
- Vectors can be multiplied by a scalar.
- Vectors cannot be multiplied by each other.
- Multiplication by a scalar can be done when the vectors are in column form.
- Multiplication by a scalar can be done when the vectors are drawn.
Vocabulary To Learn
- Scalar: A scalar is a quantity that has magnitude but not direction.
- Displacement: Displacement is the distance from the starting point when measured in a straight line.
Common Mistakes To Avoid
- A reflection of a vector in the x or y axis is not the reverse of a vector. This is often seen with equilateral triangles and vectors.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Vectors can be multiplied by a scalar. Vectors cannot be multiplied by each other.
2. Use this key word in a maths sentence and explain it clearly. 'Scalar'
A scalar is a quantity that has magnitude but not direction. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: A reflection of a vector in the x or y axis is not the reverse of a vector. This is often seen with equilateral triangles and vectors. Correction: When multiplying the vectors by -1 this gives the opposite direction of the vector only. The magnitude remains the same. Investigate with pupils by drawing column vectors and multiply by -1 and compare.
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
- Geometric proofs 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.