📘 Remember
Vectors carry both magnitude and direction. Work with horizontal and vertical components separately, and keep signs consistent.
Mixed Review
- Define a vector and give one example.
- Interpret (−4,3).
- Find AB⃗ for A(−2,1), B(5,6).
- Add (3,−2) and (−5,7).
- Calculate (8,1)−(3,−4).
- Find −3(2,5).
- Find |(8,15)|.
- If OA⃗=a and OB⃗=b, express AB⃗.
- In a parallelogram, AB⃗=p and AD⃗=q. Express DB⃗.
- Explain how vectors can prove lines are parallel.
🎯 Interactive Mixed Review
Answer each question, then mark your work.
1. If a=(3,−2) and b=(−1,4), find a+b.
2. Find |(6,8)|.
3. Vector AB for A(2,−1), B(−3,5).
4. If c=−2(3,−1), find c.
Score: 0/4
✅ Check Your Work
Show answers and working
- A quantity with magnitude and direction; e.g. force.
- Move 4 left and 3 up.
- (5−(−2),6−1)=(7,5).
- (−2,5).
- (5,5).
- (−6,−15).
- √(64+225)=17.
- b−a.
- p−q.
- Show one direction vector is a scalar multiple of the other.
⚠️ 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.
Revision Guidance and Readiness
- Attempt the questions without notes first.
- Use the answers or worked solutions to identify the exact step that needs attention.
- Return to the relevant lesson, then retry missed questions.
- You are ready to move on when you can explain your method and check your result independently.