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

- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Downloadable docs

# Chapter 11.9 - The Dot Product and Projection

# Khan Academy - Dot Product

# Khan Academy - Projection

# Dot Product and Projection

## Overview

Vectors - dot product, projection, decomposition of a vector

**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.

# Dot Product and Projection

In this section we will learn about the **dot product **of two vectors which is quite useful in higher-dimensional geometry, physics, statistics, etc. For example, dot product makes it very easy to find the shortest distance between a line and a point not on the line.

**Learning Objectives:**

- Definition of dot product
- Properties of dot product
- Geometric Interpretation of Dot Product
- Orthogonality
- Projection of a vector onto another vector
- Component of projection
- Decomposing a given vector as the sum of two orthogonal vectors
- Applications of Dot Product
- shortest distance between a point and a line.
- Force and work done
- Cauchy-Schwartz Inequality