Topic: Vectors
Subtopic: Algebraic Approach
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, u•v = (a+b)•(c+d) = ac+bd and u•v = ||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
Explore the dot product geometrically with this Java applet: www.falstad.com/dotproduct