- Subject:
- Higher Education, Mathematics, Calculus, Geometry, Physics
- Material Type:
- Module
- Provider:
- Ohio Open Ed Collaborative
- Tags:

- License:
- Creative Commons Attribution-NonCommercial 4.0
- Language:
- English
- Media Formats:
- Text/HTML

# Chapter 11.8 - Exercises

# Khan Academy - Vectors and Scalars

# Vectors in 2D

## Module Overview

Vectors - magnitude, direction, component form, trigonometric form, unit vector, algebra of vectors, applications,

**TMM 002 PRECALCULUS (Revised March 21, 2017)**

**AdditionalOptional Learning Outcomes:**

2. **Geometry**: The successful Precalculus student can:

**2e**. Interpret the result of vector computations geometrically and within the confines of a particular applied context (e.g., forces).

Sample Tasks:

- The student can define vectors, their arithmetic, their representation, and interpretations.
- The student can decompose vectors into normal and parallel components.
- The student can interpret the result of a vector computation as a change in location in the plane or as the net force acting on an object.

# Section 1: Vectors

We will learn about two-dimensional vectors which are quantities that have both magnitude and direction.

**Learning Objectives:**

- Definition of a vector and its component form
- Equality of two vectors
- Vector arithmetic and properties
- Vector Addition
- Scalar Multiplication

- Magnitude and direction of a vector, and their properties
- Unit vector
- Principal unit vector in the direction of positive x and y axes
- Writing a vector in different forms
- component form
- principal unit vector form
- magnitude and cosine and sine functions

- Application to equilibrium of forces acting on a body