Translation vector
Describes the movement of every point by the same displacement.
🎯 Learning Objectives
- identify translation, equal, negative, parallel and position vectors;
- compare vector magnitude and direction;
- represent each type diagrammatically.
Introduction
This lesson develops Types of Vectors from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Main Types of Vectors
Equal vectors
Have the same magnitude and direction, even in different positions.
Negative vectors
Have equal magnitude but opposite direction.
Parallel vectors
Have directions along parallel lines and are scalar multiples.
Position vector
Runs from the origin to a point.
Zero vector
Has magnitude zero and components (0,0).
Equal vs Negative
If a⃗=32, then −a⃗=−3−2.
🧭 Interactive Diagram: Identify the Vector Relationship
Select the best description of the two displayed vectors.
Choose a relationship, then generate another pair.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- What conditions make two vectors equal?
- How is −a⃗ related to a⃗?
- Which vector joins the origin to a point?
- Are (2,4) and (1,2) parallel?
✅ Check Your Work
Show answers and working
- They have equal magnitude and the same direction.
- Same magnitude, opposite direction.
- A position vector.
- Yes. (2,4)=2(1,2), so one is a scalar multiple of the other.
📘 Remember
Vectors carry both magnitude and direction. Work with horizontal and vertical components separately, and keep signs consistent.
⚠️ Common Mistakes
Do not confuse a point with its position vector. For AB, always calculate B − A, not A − B.
⭐ Exam Tips
Sketch arrows, label directions clearly, show component working and check whether the final direction agrees with the diagram.
🌍 Did You Know?
Vectors are used in navigation, animation, engineering, robotics, weather modelling and computer games.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.