FOCUS ON MATH
Scalar and Vector
Scalar
is a quantity which is fully described by
a magnitude alone. For example, when length
is measured, the quantity that results is
called a scalar. Vector is
a quantity which is fully described by both
magnitude and direction.
Basic Laws of Vector Algebra
A
vector A
can be written as
Where
A
is the magnitude of the vector A,
and
â
is the unit vector which has a magnitude
of unity (|â|=1),
and its direction is given by
The
unit vector in the direction of the x-axis
is i
and the unit vector in the direction of
the y-axis
is j.
The
vector A
can be represented graphically by a directed
straight-line segment of a length |A|
= A
with its arrowhead pointing in the direction
of â
as shown in Figure 1.2
Figure
1.2 A vector quantity with magnitude and
direction.
Force as an example of a Vector
A
force (F)
is a vector quantity. To fully describe
the force acting upon an object, you must
describe both the magnitude (size) and the
direction. Thus, the quantity 5 newtons
(N)
is not a full description of the force acting
upon an object. In contrast, saying “5
N
upwards” is a full description of
the force acting upon an object; both the
magnitude (5 N)
and the direction (upwards) are given. It
is common to use special notation for vector
quantities. For example F
is used for the force and |F|
for the magnitude of force. Table 1.1 classifies
few common quantities.
Table
1.1 Classification of Common Quantities
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