Chapter 11.9 - Exercises
Khan Academy - Dot Product
Khan Academy - Projection
Dot Product and Projection
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).
- 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: 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.
- Definition of dot product
- Properties of dot product
- Geometric Interpretation of Dot Product
- 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