- Author:
- Ohio Open Ed Collaborative
- 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