Lesson 1: Introduction to Vectors – Notation, Addition, Subtraction

📘 Introduction

Have you ever helped someone find their way by saying something like “go 5 steps forward, then 3 steps to the right”?
What you described is a vector — a way of showing movement using both distance and direction.
In this lesson, we’ll explore how vectors are written, how they are added or subtracted, and how we use them in everyday situations.

🧠 Key Concepts and Explanations

1. What is a Vector?

A vector is a quantity that has both:

• Magnitude (size or length)
• Direction (which way it points)

A vector is written in component form as:

where x is the horizontal movement (left/right) and y is the vertical movement (up/down).

2. Vector Notation

Common ways to represent vectors:

• Arrow notation: A → B
• Component form:
  means 4 units right, 2 units up

3. Vector Addition

To add two vectors, add their corresponding components:

4. Vector Subtraction

To subtract one vector from another, subtract the corresponding components:

🧮 Sample Problem Walkthroughs

Example 1: Adding Simple Vectors

Add
and

Solution:

Example 2: Subtracting Vectors

Find

Solution:

📝 Practice Exercises

Part A: Basic Operations

1. Add
   and
2. Subtract
   from

Part B: Word Problems

3. Angela walks 3 meters east and then 4 meters north. Represent her total displacement as a vector.
4. A car moves 5 km south and then 2 km west. What is the car’s final displacement vector?

Part C: Challenge

5. Given
   and
   , find
   

✔ Answers and Explanations

• Part A #1:
  
• Part A #2:
  
• Part B:
  • Angela:
    
  • Car:
    
• Part C:
  

🔁 Recap

• Vectors have both direction and magnitude.
• They are written using components in square brackets.
• Vector addition means adding the x and y components.
• Vector subtraction means subtracting the x and y components.
• Real-life movements can be described using vectors.

🪞 Reflection Prompt

Can you think of one movement you do every day (e.g., walking to school)?
Try to describe it using a vector. What direction and how many steps or meters would that be?