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Calculus III

Course: Trigonometry
Topic: Vectors
Subtopic: Dot Product

Overview

In that "product" means to multiply, dot product is an operation that is one way to multiply two vectors. (The other is cross product which is only performed on two 3D vectors.) There are two ways to perform the dot product, i.e. two different, but connected, dot product formulae. The result from the dot product has algebraic and geometric interpretations.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 8.3.1 Use dot product notation correctly, ie. "big dot" between two vectors (•), not the regular-sized multiplication dot (·)
• 8.3.2 Know both dot product formulas and how to apply them
• 8.3.3 Know that the answer from a dot product is a scalar not a vector
• 8.3.4 Find the dot product of two vectors algebraically and electronically
• 8.3.5 Find the angle between two vectors using the dot product formula
• 8.3.6 Determine if two vectors are perpendicular algebraically using the dot product

Terminology

Terms you should be able to define: dot product, orthogonal

Dot Product Formulas:
vecu•vecv = <<a,b>>•<<c,d>> = ac+bd
vecu•vecv = ||vecu||*||vecv||*costheta

Mini-Lectures and Examples

Supplemental Resources

Calculating the dot product manually is not difficult, but if you want to do so electronically I have directions for Texas Instruments calculators TI-86, TI-89, and TI-92 here: Prof. Keely's Calculator Guide: Vector Products.

For a visual understanding of what the dot product means geometrically explore this Java applet: www.falstad.com/dotproduct

rev. 2020-11-05