FOCUSED REVIEW
Focused Review — Vector Addition and Subtraction — Foundational
Reinforce the highest-leverage ideas and representative problem-solving tools for Vector Addition and Subtraction.
TIME
Approximately 15 minutes
BEST FOR
Targeted reinforcement
FINISH WITH
A readiness check
After this focused review, you'll be able to...
reinforce the key relationships, apply them to representative problems, and identify what still needs work.
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: Foundational
BEST USED ✓ After learning the topic ✓ Before starting homework ✓ Before a quiz or exam
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 15 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Key Ideas
Picture the sum first.
Two vectors are placed head-to-tail. Where does the resultant start and end?
Reveal Answers
It starts at the tail of the first vector and ends at the head of the last vector.
Why it works: That arrow represents the net change produced by the sequence.
ACTIVITY 2
Common Mistakes
Reverse before subtracting.
To construct A⃗ − B⃗ graphically, what change do you make to B⃗?
Reveal Answers
Reverse B⃗, then add −B⃗ to A⃗.
Why it works: Subtraction of a vector is defined as addition of its opposite.
ACTIVITY 3
Quick Application
Estimate before measuring.
A⃗ points east and B⃗ points north. In what general direction must A⃗ + B⃗ point?
Reveal Answers
Between east and north, toward the northeast.
Why it works: A correct sketch constrains the resultant direction before any calculation.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Reinforce the two highest-leverage relationships, then use them in representative situations.
KEY CONCEPT 1
Vector Addition as a Net Change
Adding vectors combines directed changes. You may slide a vector without rotating it, place vectors head-to-tail, and draw the resultant from the starting point to the ending point.
R⃗ = A⃗ + B⃗
Example: A 4 m east displacement followed by a 3 m north displacement has a resultant from the original start to the final location.
Sensei note: Keep each vector’s direction unchanged when you translate it on the page.
KEY CONCEPT 2
Vector Subtraction Uses the Opposite
To subtract a vector, reverse its direction and then use the same head-to-tail addition rule. The negative vector has the same magnitude as the original but points opposite.
A⃗ − B⃗ = A⃗ + (−B⃗)
Example: If B⃗ is 2 N west, then −B⃗ is 2 N east. Subtracting B⃗ therefore adds 2 N east.
Sensei note: The minus sign reverses the whole vector, not just its numerical label.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Apply the reinforced ideas to two representative situations, then use the strategy card to check your setup.
PRACTICE 1
Guided Example
Draw the vectors head-to-tail before answering.
A student walks 3 m east and then 4 m north. Find the magnitude and general direction of the resultant displacement.
Reveal Answers
5 m, toward the northeast.
Why it works: The two perpendicular displacements form a 3–4–5 right triangle.
PRACTICE 2
Independent Check
Reverse the second vector, then combine.
A⃗ is 6 units east and B⃗ is 2 units east. Find A⃗ − B⃗.
Reveal Answers
4 units east.
Why it works: Subtracting B⃗ is equivalent to adding 2 units west to A⃗.
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Opposite Directions
Give the resultant direction and magnitude.
A 7 N force points east and a 2 N force points west. What is the vector sum?
Reveal Answers
5 N east.
Why it works: Opposite collinear vectors subtract in magnitude, with the larger direction winning.
QUICK CHECK 2
Subtraction Meaning
State the graphical operation.
What is the first step when drawing P⃗ − Q⃗?
Reveal Answers
Reverse Q⃗ to make −Q⃗, then add it to P⃗.
Why it works: Vector subtraction is addition of the opposite vector.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
Add Head-to-Tail
The resultant runs from the initial tail to the final head and represents the net directed change.
KEY TAKEAWAY 2
Subtract by Reversing
Replace subtraction with addition of the opposite vector; preserve both magnitude and direction information.
Ready for your next step?
You've reviewed the essential ideas one last time. Now choose the resource that best matches how confident you feel. Need a quick reminder?
Next Step
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