QUICK REVIEW
Quick Review — Vector Addition and Subtraction — Algebra-Based
Refresh the essential ideas and relationships for Vector Addition and Subtraction in just a few minutes.
TIME
5–10 minutes
BEST FOR
A rapid refresh
FINISH WITH
Key ideas refreshed
After this quick review, you'll be able to...
recall the essential ideas and decide what to review next.
Choose how you want to review
Course Alignment
This Physics Sensei Topic Review is an independent learning resource. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
Related Unit Review: If you need to review the complete unit material, review Vectors and Components here →
RESOURCE: Physics Sensei Topic Review | TOPIC ID: MEC-U02-T02 | TOPIC: Vector Addition and Subtraction | PARENT UNIT: MEC-U02 — Vectors and Components | COURSE LEVEL: Algebra-Based
BEST USED ✓ After learning the topic ✓ Before starting homework ✓ Before a quiz or exam
Your Review Plan
Complete these four stages to quickly refresh the essential ideas and confirm you're ready to continue.
4 Stages • Approximately 5–10 minutes.
Quick Recall
Let's quickly refresh what you already know. These short recall activities will help you bring the most important ideas back to mind before reviewing them.
QUICK RECALL
Recall Activity
Complete the three statements from memory before revealing the answer.
Write the component rule for adding two vectors. What changes when you subtract B⃗ from A⃗?
Reveal Answers
Add matching components: Rₓ = Aₓ + Bₓ and Rᵧ = Aᵧ + Bᵧ. For A⃗ − B⃗, subtract each B component.
Why it works: Vector operations are performed independently along perpendicular component axes.
Ready to refresh the essentials?
Great! Now let's review the most important ideas you'll want to remember.
Essential Idea
Take one last look at the most important concept from this topic. If you remember this idea, the rest will come back much more easily.
ESSENTIAL IDEA
Operate on Components, Then Rebuild the Resultant
Add or subtract matching x-components and matching y-components. Once the resultant components are known, use them to find magnitude and direction, checking the quadrant before reporting the angle.
Rₓ = Aₓ ± Bₓ • Rᵧ = Aᵧ ± Bᵧ • |R⃗| = √(Rₓ² + Rᵧ²)
Example: A⃗ = (3, 4), B⃗ = (−1, 2) → A⃗ + B⃗ = (2, 6).
Sensei note: Keep the signs on every component; a negative component already carries direction.
Ready to check your memory?
You've refreshed the essential idea. Now see how much you remember before moving on. Need a quick reminder?
Confidence Check
You've refreshed the essential ideas. Now answer this quick confidence check to confirm you're ready to move on.
CONFIDENCE CHECK
Component Sum Check
Answer all three without notes.
A⃗ = (2, −1) and B⃗ = (−3, 4). Find A⃗ + B⃗.
Reveal Answers
(−1, 3).
Why it works: x: 2 + (−3) = −1; y: −1 + 4 = 3.
Ready for your next step?
Great work! You've refreshed the essential ideas. Now choose the resource that best matches what you'd like to do next. Need a quick reminder?
Next Step
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