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Addition and Geometry
Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. Scalar multiply: stretch or shrink, reverse if the scalar is negative. Section formula / midpoint: midpoint of AB is a+b2 if a,b are position vectors. Meaning: addition is 'follow one arrow, then the other'.
Choose Your Level
Addition and Geometry
What is it?
Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. Scalar multiply: stretch or shrink, reverse if the scalar is negative. Section formula / midpoint: midpoint of AB is a+b2 if a,b are position vectors. Meaning: addition is 'follow one arrow, then the other'.
In simple words
- Add vectors componentwise (or tip-to-tail / parallelogram).
- Triangle law: a + b is the third side.
- Scalar multiply: stretch or shrink, reverse if the scalar is negative.
- AB is not a+b. It is 'to B, minus to A'.
Important terms
ADDITION AND GEOMETRY: Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. Scalar multiply: stretch or shrink, reverse if the scalar is negative. Section formula / midpoint: midpoint of AB is a+b2 if a,b are position vectors. Meaning: addition is 'follow one arrow, then the other'.
1. ADD: <1,2,3>+<4,-1,0>=<5,1,3>. Parallelogram: diagonal is the sum. Subtract: a-b = a+(-b).
2. POINTS: Vector AB = b - a (position of B minus A). Length |AB| is the distance. Parallel vectors: one is a scalar times the other (components in the same ratio).
What you should learn
- State the main ideas and notation used in addition and geometry.
- Apply the rules of addition and geometry in a clear, step-by-step solution.
- Check signs, conditions, and the final answer for mathematical accuracy.
Examples
- Triangle law
- Parallelogram diagonal
- -b opposite
ADD
<1,2,3>+<4,-1,0>=<5,1,3>. Parallelogram: diagonal is the sum. Subtract: a-b = a+(-b).
POINTS
Vector AB = b - a (position of B minus A). Length |AB| is the distance. Parallel vectors: one is a scalar times the other (components in the same ratio).
Recommended for Class 11
Full school-level explanation
Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. Scalar multiply: stretch or shrink, reverse if the scalar is negative. Section formula / midpoint: midpoint of AB is a+b2 if a,b are position vectors. Meaning: addition is 'follow one arrow, then the other'.
Tip to tail, then points:
WHAT — ADDITION AND GEOMETRY
Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. Scalar multiply: stretch or shrink, reverse if the scalar is negative. Section formula / midpoint: midpoint of AB is a+b2 if a,b are position vectors. Meaning: addition is 'follow one arrow, then the other'.
RULE — 1. ADD
<1,2,3>+<4,-1,0>=<5,1,3>. Parallelogram: diagonal is the sum. Subtract: a-b = a+(-b).
METHOD — 2. POINTS
Vector AB = b - a (position of B minus A). Length |AB| is the distance. Parallel vectors: one is a scalar times the other (components in the same ratio).
WORKED EXAMPLE
Worked: AB if A is i+j and B is 4i - j + k. AB = b - a = (4i-j+k) - (i+j) = 3i - 2j + k
ADD
<1,2,3>+<4,-1,0>=<5,1,3>. Parallelogram: diagonal is the sum. Subtract: a-b = a+(-b).
Remember
- components
Examples
- Triangle law
- Parallelogram diagonal
- -b opposite
POINTS
Vector AB = b - a (position of B minus A). Length |AB| is the distance. Parallel vectors: one is a scalar times the other (components in the same ratio).
Remember
- AB = b-a
Examples
- Distance |b-a|
- Midpoint
- Parallel: a = k b
How to answer a addition and geometry question
How it works
- Identify the given quantities, notation, and required result.
- Choose the matching rule and write it before substitution.
- Work one algebraic step at a time, keeping brackets and signs clear.
- Check restrictions, simplify the result, and verify it where possible.
Remember
- add matching components
- midpoint a+b2
- 3i-2j+k
- b minus a
- components
- AB = b-a
- add matching components
- midpoint a+b2
How the ideas connect
Worked: AB if A is i+j and B is 4i - j + k. AB = b - a = (4i-j+k) - (i+j) = 3i - 2j + k
Deeper understanding
Go beyond memorising Addition and Geometry. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked: AB if A is i+j and B is 4i - j + k. AB = b - a = (4i-j+k) - (i+j) = 3i - 2j + k
Common mistakes
Exam focus
Core Idea
1. ADD
2. POINTS
Worked Example
Exam focus
Quick revision
- add matching components
- midpoint a+b2
- 3i-2j+k
- b minus a
- ADDITION AND GEOMETRY: Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. S
- 1. ADD: <1,2,3>+<4,-1,0>=<5,1,3>. Parallelogram: diagonal is the sum. Subtract: a-b = a+(-b).
AB is not a+b. It is 'to B, minus to A'.
For long answers on Addition and Geometry: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- add matching components
- midpoint a+b2
- 3i-2j+k
- b minus a
Important formulas
- add matching components
- midpoint a+b2
- 3i-2j+k
Common exam traps
- AB is not a+b. It is 'to B, minus to A'.
- Do not use a remembered formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
AB is not a+b. It is 'to B, minus to A'.
- Mistake
Do not use a remembered formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes or restrictions; write them on the line where they are used.
- Mistake
AB is not a+b. It is 'to B, minus to A'.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
add matching components
midpoint a+b2
3i-2j+k
b minus a
Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. Scalar multiply: stretch or shrink, reverse if the scalar is
AB = b-a
- Definition
- Add vectors componentwise (or tip-to-tail / parallelogram). Triangle law: a + b is the third side. Scalar multiply: stretch or shrink, reverse if the scalar is
- Formula
- AB = b-a
- Example
- Triangle law
- Critical warning
- AB is not a+b. It is 'to B, minus to A'.
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Exam Practice
Define
Q1. Define Addition and Geometry.
Explain
Q2. Explain: ADD.
Example
Q3. Give one clear example of Addition and Geometry and say why it fits.
Mistake
Q4. State one common mistake students make about Addition and Geometry.
Exam note
Q5. Write a short exam note on Addition and Geometry: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.