Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
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Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
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Trigonometry
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Calculus II
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15.Functions of Several Variables
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17.Vector Analysis

Course: Trigonometry
Topic: Vectors
Subtopic: Algebraic Approach and Dot Product

Overview

We previously introduced vectors geometrically. In this lesson we approach vectors algebraically, e.g. adding vectors is accomplished using their algebraic vector representations. There is more vector terminology to learn, and several theorems and formulas to apply. One process of particular importance is the dot product of two vectors.

Objectives

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

• 8.2.1 Use correctly both vector notations
• 8.2.2 Perform vector operations (addition, subtraction, and scalar multiplication) algebraically
• 8.2.3 Find a vector's magnitude and direction algebraically
• 8.2.4 Know both dot product formulas, uv = (a+b)•(c+d) = ac+bd and uv = ||u|| ||v|| cosθ, and how to apply them
• 8.2 5 Find the dot product of two vectors algebraically and electronically
• 8.2.6 Find the angle between two vectors using the dot product formula
• 8.2 7 Determine if two vectors are perpendicular algebraically using the dot product
• 8.2.8 Determine if two vectors are parallel algebraically by determining if one is a scalar multiple of the other

Terminology

Define: unit vector, unit horizontal vector, unit vertical vector, basic unit vectors, orthogonal, normal vector, scalar product, dot product

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