**Vector Analysis**

*
Mark A. Strain, PE
*

**
Course Outline**

Vector analysis is a mathematical tool used to explain and predict physical phenomena in the study of mechanics. A vector is a depiction or symbol showing movement or a force carried from point A to point B. A vector has properties of both magnitude and direction. A scalar only has the property of magnitude.

The purpose of this course is to describe vectors and to explain their use and to demonstrate their many applications. This course also describes several vector operations including the dot product and cross product.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

**
Learning
Objective **

At the conclusion of this course the student will learn:

- How to apply the use of vectors to different fields of engineering;
- How to decompose a vector into its individual components;
- How to find the length of a vector;
- How to compute the dot product of a vector;
- How to compute the cross product of a vector; and
- How to determine the angle between two vectors.

** Intended
Audience**

This course is intended for all engineers.

** Benefit to Attendees**

Attendee of this course will be able to understand the fundamentals of vector analysis.

**Course Introduction**

Mechanics is the science of motion and the study of the action of forces on bodies. Mechanics is a physical science incorporating mathematical concepts directly applicable to many fields of engineering such as mechanical, civil, structural and electrical engineering.

Vector analysis is a mathematical tool used in mechanics to explain and predict physical phenomena. The word “vector” comes from the Latin word *vectus* (or *vehere* – meaning to carry). A vector is a depiction or symbol showing movement or a force carried from point A to point B.

A scalar is a quantity, like mass (14 kg), temperature (25°C), or electric field intensity (40 N/C) that only has magnitude and no direction. On the other hand, a vector has both magnitude and direction. Physical quantities that have magnitude and direction can be represented by the length and direction of an arrow.

**Course
Content**

This course is in the following PDF document:

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** Course Summary**

Vector mechanics is the application of vectors in the science of mechanics. Mechanics is the science of motion and the study of the action of forces on bodies. Vector analysis is very important in many fields of engineering such as mechanical, civil, structural and electrical engineering.

Scalar values, such as mass and temperature convey only a magnitude, but vectors such as velocity employ both a magnitude and a direction. The dot product is a vector operation on two vectors that produces a scalar value. The dot product is used to find the angle between two vectors or to find the projection of a vector onto a line. The cross product is a vector operation on two vectors that produces another vector. The cross product may be used to calculate the moment of a force around a point at a given radius.

**Quiz **

**Once
you finish studying ****the
above course content,****
you need to
take a quiz
to obtain the PDH credits**.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.