Chapter
Introduction to Vectors
Scalars are quantities with magnitude only whereas vectors are those quantities
having both a magnitude and a direction. Vectors are used to model a variety
of fundamental processes occurring in engineering, physics and the sciences. The
material presented in the pages that follow investigates both scalar and vectors
quantities and operations associated with their use in solving applied problems. In
particular, differentiation and integration techniques associated with both scalar and
vector quantities will be investigated.
Vectors and Scalars
A vector is any quantity which possesses both magnitude and direction.
A scalar is a quantity which possesses a magnitude but does not possess
a direction.Examples of vector quantities are force, velocity, acceleration, momentum,
weight, torque, angular velocity, angular acceleration, angular momentum.
Examples of scalar quantities are time, temperature, size of an angle, energy,
mass, length, speed, density
Figure 6-1.
Scalar multiplication.
A vector can be represented by an arrow. The
orientation of the arrow determines the direction ofthe vector, and the length of the arrow is associated
with the magnitude of the vector. The magnitude
of a vector B is denoted |B |or B and represents
the length of the vector. The tail end of the arrow
is called the origin , and the arrowhead is called the
terminus. Vectors are usually denoted by letters in
bold face type. When a bold face type is inconve-
nient to use, then a letter with an arrow over it
is employed, such as, A, B, C. Throughout this text the arrow notation is used in
all discussions of vectors.
Properties of Vectors