# Vector Analysis Fundamentals

Mark A. Strain, P.E. ## Course Overview

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. 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.

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. Vectors are tools used in the study of mechanics.

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.

## Learning Objectives

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
• How to determine the angle between two vectors