QUICK REVIEW
Quick Review — Vector Addition and Subtraction — Calculus-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: Calculus-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.
State the component rule for A⃗ ± B⃗ in a fixed basis, and explain why the same rule applies to position-vector differences.
Reveal Answers
A⃗ ± B⃗ = (Aₓ ± Bₓ)e₁ + (Aᵧ ± Bᵧ)e₂. The same component-wise rule gives Δr⃗ = r⃗₂ − r⃗₁.
Why it works: Vector addition and scalar multiplication are linear operations in the chosen basis.
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
Vector Addition and Subtraction Are Linear Operations
In a fixed basis, add or subtract corresponding components. A position difference uses the same operation: subtract the initial position vector from the final position vector to obtain a displacement that does not depend on the chosen origin.
A⃗ ± B⃗ = (Aₓ ± Bₓ)e₁ + (Aᵧ ± Bᵧ)e₂
Example: r⃗₁ = (2, −1), r⃗₂ = (−1, 3) → Δr⃗ = r⃗₂ − r⃗₁ = (−3, 4).
Sensei note: Subtract the entire vector function or vector expression component by component.
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
Linear Combination Check
Answer all three without notes.
A⃗ = (1, 2), B⃗ = (−2, 1). Find 2A⃗ − B⃗.
Reveal Answers
(4, 3).
Why it works: 2A⃗ = (2, 4); subtracting B⃗ gives (2 − (−2), 4 − 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
Great work!
You've completed this review. Choose the next resource that best matches how confident you feel.
I'm Still Unsure
Review the key ideas and examples again.
Review Again →
I Need More Practice
Continue with additional practice for this topic.
Go to Practice →
I'm Ready
Continue to the next recommended resource.
Continue →