Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
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
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis

Course: Calculus III
Topic: Vectors and Geometry of Space
Subtopic: Rectangular Coordinates and Vectors in 3D

Overview

Giving our graphs some dimension, to day we expand our graphs from a 2D system to a 3D system with x-axis, y-axis, and z-axis. No longer are we constrained to four quadrants as now we can graph lines, curves, planes, and 3D shapes in all eight octants. Additionally, we look at vectors in 3D. All the operations and processes that we can do with vectors in a plane (2D vectors) we will now perform on vectors in space (3D vectors). Visually appealing fun stuff!

Objectives

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

• 13.2.1 Know terminology related to a 3D axis system (eg. yz-plane) and understand what it means to be a right-handed system
• 13.2.2 In a 3D system plot points, find distance between two points, find the midpoint of the line segment spanning two points
• 13.2.3 Given the equation of a plane, sketch it on a 3D system
• 13.2.4 Given the sketch of a plane in 3D or given information about a plane in 3D, find its equation
• 13.2.5 Determine from the sketch and/or equations if two planes are parallel or not
• 13.2.6 Given the equation of a sphere or ball, sketch it on a 3D system
• 13.2.7 Given the sketch of a sphere or ball in 3D or given information about a sphere or ball in 3D, find its equation
• 13.2.8 Perform vector operations on vectors in 3D
• 13.2.9 Do all the things that we learned to do on 2D vectors in the plane now on 3D vectors in space including find magnitude, direction, and a unit vector in the direction of a given vector

Terminology

Define: three-dimensional rectangular coordinate system, right-handed systems, octant, ordered triple, sphere, ball, ℝ3

Formulae to have in your notes: distance, midpoint

Supplemental Resources (recommended)

Need a 3D grapher? See recommendations at "Online 3D Graphers (free!)" at Where can I find a free online grapher, graphing software, or graphing app?.

Supplemental Resources (optional)

Paul's OL Notes - Calc III: The 3D Coordinate System

Patrick JMT Just Math video tutorials: PatrickJMT.com/#calculus
I'm not recommending this site today since the vector examples tend to be 2D, not 3D. Instead see ...

James Sousa's Math Is Power 4U video tutorials: MathIsPower4U - Calc II
Scroll down the third column to the "Vectors in Space" category. The first 10+ vectors listed are useful for this unit. Stop at "Dot Product" which is covered in our next unit.