MATHEMATICS VECTOR GEOMETRY REVISION.pptx

Scalar multiples
Vector addition
Collinearity

1. KAZIBA STEPHEN VECTORS 25 TH AUGUST 2025

2. OVERView Introduction Addition of vectors Subtraction of Vectors Position vectors and Column vectors Unknown vectors(Finding) Mid points of lines Division of lines (Internal and External Parallelism Collinearity 2

3. NOTE ARROWS LINES VECTOR SYMBOLS UNITS 3

4. Introduction – ACTIVITY 1 A boat is heading north from one shore to the other at a constant speed of 4km/h . The water current flows east at a constant speed of 3km/h . Where will the boat actually end up? What will be the actual path of the boat? What is the vector (per hour) of: The boat’s heading (in km)? The current displacement (in km)? The actual path of the boat (in km)? 4 4 km 1 km Heading of the boat Current displacement Actual path      

5. Introduction – ACTIVITY 2 A boat is heading east at a constant speed of 3km/h . The water current flows east at a constant speed of 2km/h . Where will the boat actually end up after 1 hour? What will be the actual path of the boat? What is the vector (per hour) of: The boat’s heading (in km)? The current displacement (in km)? The actual path of the boat (in km)? 5 1 km 1 km Heading of the boat Current displacement Actual path      

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12. Collinear Points 12

13. Item City planners are designing a new straight road that should pass through three important locations: P  (-3, -2): An existing bus terminal Q  (3, 1): A proposed shopping mall R  (5, 2): A planned hospital The planners need to verify if these three points lie on a straight line to ensure the road can be built in a single straight segment. This will save construction costs and improve efficiency. Task: Guide the planners whether they should proceed with the construction of the road .What is the distance between the Bus terminal and shopping mall. Levae your answer in a simplified surd. 13

14. Item City planners are designing a new straight road that should pass through three important locations: P  (-3, -2): An existing bus terminal Q  (3, 1): A proposed shopping mall R  (5, 2): A planned hospital The planners need to verify if these three points lie on a straight line to ensure the road can be built in a single straight segment. This will save construction costs and improve efficiency. Task: Guide the planners whether they should proceed with the construction of the road .What is the distance between the Bus terminal and shopping mall. Leave your answer in a simplified surd. 14

15. Item City planners are designing a new straight road that should pass through three important locations: P  (-3, -2): An existing bus terminal Q  (3, 1): A proposed shopping mall R  (5, 2): A planned hospital The planners need to verify if these three points lie on a straight line to ensure the road can be built in a single straight segment. This will save construction costs and improve efficiency. Task: Guide the planners whether they should proceed with the construction of the road .What is the distance between the Bus terminal and shopping mall. Leave your answer in a simplified surd. 15

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