0.31 Phy1310: vector multiplication

Table of contents

• Preface
  • General
  • Prerequisites
  • Viewing tip
    • Figures
  • Supplemental material
• Discussion
  • Dot product, inner product, or scalar product
    • Background
    • Create a vector diagram on your graph board
    • The dot product
    • The projection of A onto B
    • Compute the projection
    • Compute the angle between the vectors
    • Perpendicular or parallel vectors
    • Summary for vector dot product
  • Cross product
    • Background
    • The right-hand rule
    • Create a vector diagram on your graph board
    • The cross product
    • The area of the parallelogram
    • The direction of the resultant vector
    • Perpendicular or parallel vectors
    • Summary for vector cross product
• Repeat the computations
• Resources
• Miscellaneous

Preface

General

This module is part of a book (or collection) designed to make physics concepts accessible to blind students. The collection is intended to supplement but not to replace thetextbook in an introductory course in high school or college physics.

This module explains vector multiplication in a format that is accessible to blind students.

Prerequisites

In addition to an Internet connection and a browser, you will need the following tools (as a minimum) to work through the exercises in these modules:

• A graph board for plotting graphs and vector diagrams ( (External Link) ).
• A protractor for measuring angles ( (External Link) ).
• An audio screen reader that is compatible with your operating system, such as the NonVisual Desktop Access program (NVDA), which is freelyavailable at (External Link) .
• A refreshable Braille display capable of providing a line by line tactile output of information displayed on the computer monitor ( (External Link) ).
• A device to create Braille labels. Will be used to label graphs constructed on the graph board.

The minimum prerequisites for understanding the material in these modules include:

• A good understanding of algebra.
• An understanding of the use of a graph board for plotting graphs and vector diagrams ( (External Link) ).
• An understanding of the use of a protractor for measuring angles ( (External Link) ).
• A basic understanding of the use of sine, cosine, and tangent from trigonometry ( (External Link) ).
• An introductory understanding of JavaScript programming ( (External Link) and (External Link) ).
• An understanding of all of the material covered in the earlier modules in this collection.

Viewing tip

I recommend that you open another copy of this document in a separate browser window and use the following links to easily find and view the figures while you are reading about them.

Figures

• Figure 1 . Facts worth remembering for the dot product.
• Figure 2 . Facts worth remembering for the cross product.

Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

Discussion

You learned about vector addition and vector subtraction in earlier modules. It is also possible to multiply vectors. That capability will become importantin future modules.