This lesson introduces you to three-dimensional rectangular coordinates systems, distance and midpoint formulas in three dimensions, and how to identify, describe, and sketch simple 3D objects.
View all of the instructional videos, read the provided readings, and practice exercise/activities. These will help you master the objectives for this lesson. Pay attention to additional comments provided. Practice to visualize the problem that you have to solve in xyz-space.
Upon completion of lesson 1.2, you will be able to:
Identify and plot points and projections of points
Identify and sketch planes
Identify and sketch simple 3D objects
Find equation or inequality describing simple 3D objects
Determine distance and midpoint
View all of the following instructional videos. These will help you master the objectives for this lesson.
Warning: The presenter speaks fast in the videos below, so you need to be really focused.
Calculus III: Three Dimensional Coordinate Systems (Level 1) [10:38]
Introduction to the 3-dimentional coordinate system and points in space
Source: Mathfortress from YouTube
Note: At about 9:00, you may want to pause the video and copy down the coordinates of the points, so that it will be easier to follow.
Calculus III: Three Dimensional Coordinate Systems (Level 2) [10:22]
Coordinate planes, planes parallel to an axis, projections of a point onto the coordinate planesSource:
Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 3) [10:32]
Graph simple equations in R3
Source: Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 4) [10:52]
The midpoint formula and the distance formula in R3
Source: Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 5) [10:48]
Finding distance between 2 points in space, determining collinear points, introducing equation of a sphere
Source: Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 6) [10:28]
Application of distance formula
Source: Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 7) [6:50]
Three basic examples of spheres
Source: Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 8) [9:56]
Three intermediate examples of spheres
Source: Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 9) [8:12]
Two challenging examples of spheres
Source: Mathfortree from YouTube
Calculus III: Three Dimensional Coordinate Systems (Level 10) [11:37]
Graphing inequalities in R3
Source: Mathfortree from YouTube
The following required readings cover the content for this lesson. As you go through each reading, pay close attention to the content that will help you learn the objectives for this lesson.
Three-Dimensional Coordinate Systems Jim Lambers
Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.
Note: You can practice problems Variant #1, Variant #2, and also the first problem in the Mini Test. You may practice other problems when you take Calculus IV.
Massey University
Practice Mini-Test 1 and answers (Calculus 3 - Spring 2004) PDF
Dr. Steven Bellenot, Florida State University - Mathematics
Note: The first two questions of the Mini-Test are related to this lesson, furthermore, the other questions are useful practice for other lessons as well.
Below are additional resources that help reinforce the content for this module.
Equation of a Sphere (video) [9:40]
Source: bullcleo1 from YouTube
The Distance Formula in 3-Dimensions (video) [2:07]
Source: patrickJMT from YouTube
Plotting Points in 3D (video) [10:38]
Source: bullcleo1 from YouTube
Do Homework 1.2 on MyMathLab.
Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.