Mastering Vectors: Adding and Subtracting with Magnitude

Mastering Vectors: Adding and Subtracting with Magnitude

Learning Objective

At the end of the lesson you will be able to use i and j and column vector notation, add and subtract vectors, and use Pythagoras theorem to calculate the magnitude of the vector.

What do you already know about vectors?

Introduction to Vectors

Vectors are quantities that have both magnitude and direction. They are represented by arrows and can be manipulated mathematically.

i and j Notation

i and j are unit vectors in the x and y direction respectively. They are used to represent components of a vector in 2D space.

Column Vector Notation

Vectors can be represented as column matrices, with their components listed in a vertical arrangement.

Adding Vectors

To add vectors, simply add their corresponding components. The resulting vector is the sum of the individual vectors.

Subtracting Vectors

Subtracting vectors involves subtracting their corresponding components. The resulting vector is the difference between the individual vectors.

Magnitude of a Vector

The magnitude of a vector represents its length and is calculated using the Pythagorean theorem in 2D space.

Definition of Magnitude

Magnitude is the size of a vector, representing the distance from the starting point to the end point of the vector.

Practice Questions

Solve the following vector problems: 1. Add the vectors A = 3i + 2j and B = -i - 4j. 2. Find the magnitude of the vector V = 5i + 12j.

Plenary: Multiple Choice Activity

Which of the following is used to represent the components of a vector in 2D space? A) i and j notation B) Column vector notation C) Magnitude D) Pythagorean theorem

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.