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


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!


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


Terms you should be able to 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.