Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Define position vectors in the Cartesian plane.
• Express points as position vectors.
• Calculate the position vector of a point from its coordinates.
• Understand the meaning of position vectors in real-life.

Lesson summary

This lesson serves as a bridge between two topics learners are familiar with: plotting points on the Cartesian plane and the basic idea of vectors. We will learn how to describe the exact location of any point on a graph not just with coordinates like (x, y), but as a journey from a starting point. This "journey" is called a position vector. Think of giving directions in your town. If you tell someone to meet you at the market, you might say, "Start from the big roundabout, walk 200 metres towards the post office, then turn and walk 100 metres towards the school." The roundabout is your starting point, your origin. The description of the journey is the vector.

Lesson notes

Part 1: Recap of the Cartesian Plane

Before we discuss vectors, let's remember the Cartesian plane. It is a flat surface (like a page in your exercise book) with two perpendicular number lines: the horizontal x-axis and the vertical y-axis. The point where they cross is called the Origin, and its coordinates are (0, 0). Any point on the plane can be described by an ordered pair of numbers called coordinates (x, y). The first number, x, tells us how far to move along the x-axis (right for positive, left for negative). The second number, y, tells us how far to move along the y-axis (up for positive, down for negative).

Example: The point A(4, 3) means: from the origin (0,0), move 4 units to the right, and then 3 units up. Part 2: Introduction to Position Vectors

A vector is a quantity that has both magnitude (size or length) and direction. A position vector is a special type of vector that describes the position of a point *relative to the origin (0, 0)*. It always starts at the Origin (O). It ends at the point in question (let's call it P). We can represent the position vector of point P as $\overrightarrow{OP}$. The arrow shows the direction is from O to P. Part 3: Connecting Coordinates to Column Vectors