SlideShare a Scribd company logo
Vectors
Audrey Pramesti and Hanna Tamba
Properties
➔ Has magnitude and direction
➔ Notation of vectors
ā -ā 2ā
A B
Addition and Subtraction of Vectors
1. Parallelogram Method
2. Polygon method
ā ē
becomes
ā+ē
ā
ē becomes
ā+ē
➔ PA=CB because PA//CB
➔ CB=a, CD=b, so CP= a+b
➔ PA=EF= a
➔ CP=DE= a+b
➔ FD=FE+ED= (-a) + (-a-b) = -2a - b
Titik P adalah titik pusat segi enam
beraturan ABC.DEF. JIka PA=a dan
CD=b, maka FD=?
E D
CF
BA
P
Answer: - 2a - b
OP = OA + AP
= OA + 1/3 AB
= OA + 1/3 (AO + OB)
= a + 1/3 (-a + b)
= a - 1/3 a + 1/3 b
= 2/3 a + 1/3 b
Diketahui persegi panjang OABC dan D titik
tengah OA, CD memotong diagonal AB di P. jika
OA = A dan OB = B maka OP dapat dinyatakan
sebagai...

More Related Content

What's hot

Assignment # 5
Assignment # 5Assignment # 5
Assignment # 5
Aya Chavez
 
Obj. 19 Coordinate Proof
Obj. 19 Coordinate ProofObj. 19 Coordinate Proof
Obj. 19 Coordinate Proof
smiller5
 
Prove it! (circles)
Prove it! (circles)Prove it! (circles)
Prove it! (circles)
Frank Davis
 
Sec 2 Term 3 Arc Length 01 97
Sec 2   Term 3 Arc Length 01  97Sec 2   Term 3 Arc Length 01  97
Sec 2 Term 3 Arc Length 01 97
JoyceXiao
 
Formulario+cuerpos+geométricos
Formulario+cuerpos+geométricosFormulario+cuerpos+geométricos
Formulario+cuerpos+geométricos
ariel
 
Trigonometry [QEE-R 2012]
Trigonometry [QEE-R 2012]Trigonometry [QEE-R 2012]
Trigonometry [QEE-R 2012]
Vanny Rose Martin
 
Pizza Problem
Pizza ProblemPizza Problem
Pizza Problem
HC Wong
 
Trigonometric Problems
Trigonometric ProblemsTrigonometric Problems
Trigonometric Problems
aluahp
 
Prove it!
Prove it!Prove it!
Prove it!
Frank Davis
 
8 2 Using Properties Of Parallelograms
8 2 Using Properties Of Parallelograms8 2 Using Properties Of Parallelograms
8 2 Using Properties Of Parallelograms
guestd1dc2e
 
Pythagoras Theorem and Proof
Pythagoras Theorem and ProofPythagoras Theorem and Proof
Pythagoras Theorem and Proof
Ronnith Nandy
 
Tema 8 areas y volúmenes
Tema 8   areas y volúmenesTema 8   areas y volúmenes
Tema 8 areas y volúmenes
Nadia Gonzalez
 
Formulas Perimeter and Area 10 7,8,10,11
Formulas Perimeter and Area 10 7,8,10,11Formulas Perimeter and Area 10 7,8,10,11
Formulas Perimeter and Area 10 7,8,10,11
katiavidal
 
Trigono
TrigonoTrigono
Trigono
vanialundina
 
Geometry - Altitude of triangle
Geometry - Altitude of triangle Geometry - Altitude of triangle
Geometry - Altitude of triangle
2IIM
 
Proof of the property
Proof of the propertyProof of the property
Proof of the property
njcjh306groupd
 
Quadrilaterals
QuadrilateralsQuadrilaterals
Quadrilaterals
Harsh Singh
 

What's hot (17)

Assignment # 5
Assignment # 5Assignment # 5
Assignment # 5
 
Obj. 19 Coordinate Proof
Obj. 19 Coordinate ProofObj. 19 Coordinate Proof
Obj. 19 Coordinate Proof
 
Prove it! (circles)
Prove it! (circles)Prove it! (circles)
Prove it! (circles)
 
Sec 2 Term 3 Arc Length 01 97
Sec 2   Term 3 Arc Length 01  97Sec 2   Term 3 Arc Length 01  97
Sec 2 Term 3 Arc Length 01 97
 
Formulario+cuerpos+geométricos
Formulario+cuerpos+geométricosFormulario+cuerpos+geométricos
Formulario+cuerpos+geométricos
 
Trigonometry [QEE-R 2012]
Trigonometry [QEE-R 2012]Trigonometry [QEE-R 2012]
Trigonometry [QEE-R 2012]
 
Pizza Problem
Pizza ProblemPizza Problem
Pizza Problem
 
Trigonometric Problems
Trigonometric ProblemsTrigonometric Problems
Trigonometric Problems
 
Prove it!
Prove it!Prove it!
Prove it!
 
8 2 Using Properties Of Parallelograms
8 2 Using Properties Of Parallelograms8 2 Using Properties Of Parallelograms
8 2 Using Properties Of Parallelograms
 
Pythagoras Theorem and Proof
Pythagoras Theorem and ProofPythagoras Theorem and Proof
Pythagoras Theorem and Proof
 
Tema 8 areas y volúmenes
Tema 8   areas y volúmenesTema 8   areas y volúmenes
Tema 8 areas y volúmenes
 
Formulas Perimeter and Area 10 7,8,10,11
Formulas Perimeter and Area 10 7,8,10,11Formulas Perimeter and Area 10 7,8,10,11
Formulas Perimeter and Area 10 7,8,10,11
 
Trigono
TrigonoTrigono
Trigono
 
Geometry - Altitude of triangle
Geometry - Altitude of triangle Geometry - Altitude of triangle
Geometry - Altitude of triangle
 
Proof of the property
Proof of the propertyProof of the property
Proof of the property
 
Quadrilaterals
QuadrilateralsQuadrilaterals
Quadrilaterals
 

Recently uploaded

CACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdfCACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdf
camakaiclarkmusic
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat  Leveraging AI for Diversity, Equity, and InclusionExecutive Directors Chat  Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
TechSoup
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
Colégio Santa Teresinha
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
adhitya5119
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Nicholas Montgomery
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Celine George
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
Celine George
 
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
IreneSebastianRueco1
 
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHatAzure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Scholarhat
 
Assessment and Planning in Educational technology.pptx
Assessment and Planning in Educational technology.pptxAssessment and Planning in Educational technology.pptx
Assessment and Planning in Educational technology.pptx
Kavitha Krishnan
 
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
RitikBhardwaj56
 
The Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collectionThe Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collection
Israel Genealogy Research Association
 
World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024
ak6969907
 
S1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptxS1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptx
tarandeep35
 
Top five deadliest dog breeds in America
Top five deadliest dog breeds in AmericaTop five deadliest dog breeds in America
Top five deadliest dog breeds in America
Bisnar Chase Personal Injury Attorneys
 
The basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptxThe basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptx
heathfieldcps1
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
Dr. Shivangi Singh Parihar
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
AyyanKhan40
 

Recently uploaded (20)

CACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdfCACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdf
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat  Leveraging AI for Diversity, Equity, and InclusionExecutive Directors Chat  Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
 
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
 
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHatAzure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
 
Assessment and Planning in Educational technology.pptx
Assessment and Planning in Educational technology.pptxAssessment and Planning in Educational technology.pptx
Assessment and Planning in Educational technology.pptx
 
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
 
The Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collectionThe Diamonds of 2023-2024 in the IGRA collection
The Diamonds of 2023-2024 in the IGRA collection
 
World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024
 
S1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptxS1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptx
 
Top five deadliest dog breeds in America
Top five deadliest dog breeds in AmericaTop five deadliest dog breeds in America
Top five deadliest dog breeds in America
 
The basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptxThe basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptx
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
 

Vektor

  • 2. Properties ➔ Has magnitude and direction ➔ Notation of vectors ā -ā 2ā A B
  • 3. Addition and Subtraction of Vectors 1. Parallelogram Method 2. Polygon method ā ē becomes ā+ē ā ē becomes ā+ē
  • 4. ➔ PA=CB because PA//CB ➔ CB=a, CD=b, so CP= a+b ➔ PA=EF= a ➔ CP=DE= a+b ➔ FD=FE+ED= (-a) + (-a-b) = -2a - b Titik P adalah titik pusat segi enam beraturan ABC.DEF. JIka PA=a dan CD=b, maka FD=? E D CF BA P Answer: - 2a - b
  • 5. OP = OA + AP = OA + 1/3 AB = OA + 1/3 (AO + OB) = a + 1/3 (-a + b) = a - 1/3 a + 1/3 b = 2/3 a + 1/3 b Diketahui persegi panjang OABC dan D titik tengah OA, CD memotong diagonal AB di P. jika OA = A dan OB = B maka OP dapat dinyatakan sebagai...