Multiplying Vectors  Multiplying a Vector by a Scalar
The product of a vector
and a scalar s is a new vector, whose direction is the same as that of
if s
is positive or opposite to that direction if s is negative (see Figure 3.8). The magnitude of the new
vector is the magnitude of
multiplied by the absolute value of s. This procedure can be
summarized as follows:
Figure 3.8. Multiplying a vector by a scalar.
Since two vectors are only equal only if their corresponding components are equal, we obtain the
following relation between the components of
and the components of
:
The following relations are summarizing the relations between the magnitude and direction of
the vectors
and
:
3.3. Multiplying Vectors  Scalar Product
Two vectors
and
are shown in Figure 3.9. The angle between these two vectors is [phi]. The
scalar product of
and
(represented by
.
) is defined as:
In a coordinate system in which the x, y and zaxes are mutual perpendicular, the following
relations hold for the scalar product between the various unit vectors:
Suppose that the vectors
and
are defined as follows:
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 Fall '09
 Dot Product, Vector Product, scalar product, Righthand rule

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