Course: Calculus III
Topic: Vectors and Geometry of Space
Subtopic: Vectors in 2D


A vector looks like a little ray, lies in two or three (or higher) dimensions, has length and direction, and can be used to represent things like velocity or force. You likely 2D vectors in a Precalculus math course. It may help to review particularly the list of objectives (to be sure that you know all that you should) listed in my College Trigonometry Lesson Notes TRIG #8.1, TRIG #8.2, TRIG #8.3, TRIG #8.4. Here in Calculus we will quickly re-introduce 2D vectors, vector terminology, vector operations, and some basic applications before expanding these concepts to 3D vectors, and ultimately moving to the Calculus of Vectors.


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


Terms you should be able to define: vector, magnitude, direction, equal vectors, zero vector, scalar, scalar multiple, position vectors, vector components, unit vector, standard basis vectors (a.k.a. coordinate unit vectors), equilibrium

Formulae to have in your notes: magnitude of a vector

Supplemental Resources (recommended)

Download: Briggs Calc for STEM's Multivariable Study Card If you print this it is only page 1 and half of page 2 that is used in this course. Most of the rest is used in Calc IV.

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Vectors - The Basics and Vector Arithmetic

Patrick JMT Just Math video tutorials: PatrickJMT.com/#calculus
Scroll down the third column to videos starting with "An Introduction to Vectors, Part 1".

James Sousa's Math Is Power 4U video tutorials: MathIsPower4U - Calc II
Scroll down the third column to the "Vectors" category. All of the videos listed there are applicable to this unit.