U6 Vectors(KA/PRE/U6)

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Unit 6: Vectors

Vectors Introduction

A vector has both magnitude and direction, represented by an arrow in space.

Vector Components

A vector can be broken down into horizontal (x) and vertical (y) components.

Magnitude of Vectors

Magnitude = √(x² + y²)

Scalar Multiplication

Scaling a vector changes its magnitude but not its direction.

Vector Addition and Subtraction

Vectors are added by adding their components.

Direction of Vectors

Direction is the angle the vector makes with the x-axis: θ = arctan(y/x)

Vector Components from Magnitude and Direction

x = magnitude * cos(θ), y = magnitude * sin(θ)

Adding Vectors in Magnitude and Direction Form

Convert to components, add components, convert back to magnitude and direction.

Vectors Word Problems

Vectors are used in navigation, physics (forces), engineering, and more.

Quiz: Test Your Understanding

If vector A = (3, 4), what is its magnitude?

  1. 5
  2. 7
  3. 25

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