Section 8.4 Vectors
In this section, we study vectors. Vectors are very useful mathematical tools, and they are especially
important for the study of physical applications of mathematics.
A
vector
, denoted in these notes in boldface, like
v
, is a quantity that has both
magnitude and
direction
. Vectors are frequently represented by arrows. When a vector
v
is represented by an
arrow, the length of the arrow indicates the
magnitude
and the direction of the arrow indicates
the direction of the vector. The magnitude of
v
is denoted by

v

.
If
v
is a vector and

v

=1
,then
v
is called a
unit vector
.A
position vector
is a vector that
has its initial point (tail) at the origin. The
zero vector
, indicated by
0
, is the vector having
magnitude equal to zero. Two vectors are
equal
if they have equal magnitude and direction. If
u
and
v
are equal, we write
u=v
. We do not distinguish between translates of vectors; hence, two
parallel vectors of equal length pointing in the same direction are equal.
We give some examples to show the diﬀerence between vectors and
scalars
(numbers). The number
3 has magnitude but not direction. Hence, the number 3 is a scalar and not a vector. The velocity
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 Kutter
 Algebra, Addition, Vectors, Vector Space, Dot Product, Force, αV

Click to edit the document details