Subject:
Engineering, Higher Education, Mathematics, Geometry, Trigonometry
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Area of a Triangle, Component of Projection, Decompostion of a Vector, Dot Products, Force, Normal Vector, Projection, Tmm0022, Unit Vector, Work
Language:
English
Media Formats:

# Dot Product and Projection

## Overview

Vectors - dot product, projection, decomposition of a vector

TMM 002 PRECALCULUS (Revised March 21, 2017)

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).

• 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