<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

Chapter 5: Vectors

Difficulty Level: At Grade Created by: CK-12


We use vectors to describe how different forces work together. They can be thought of as measures of "shared contribution" to a specific goal, usually a speed or distance traveled.

For instance, consider a boat traveling across a stream. The boat would be pushed straight across by the motor, but the current of the stream would be pushing it sideways to that motion, so the result would be a diagonal direction. In this example, the push of the motor and the push of the current would each be a vector, resulting in the diagonal travel direction.

Vector calculations can be used in a vast number of different situations, to combine or separate different contributions to a total.

Chapter Outline

Chapter Summary


This chapter is a reasonably in-depth exploration of the uses of vectors. The information begins with a study of 2-dimensional vectors and the calculation of midpoint and location in a 2-dimensional plane, and progresses through similar topics in 3-dimensions.

Students are later introduced to dot-products and cross-products and the uses for each, and the associated applications of scalar and vector projections.

The last few lessons cover the calculation of the distance of a plane from the origin, and the vector equation of a line, before summing up with examples of vector analysis in real-world situations.

Image Attributions

Show Hide Details
Difficulty Level:
At Grade
Date Created:
Nov 01, 2012
Last Modified:
Mar 23, 2016
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the FlexBook® textbook. Please Customize the FlexBook® textbook.
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original