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VectorCalc User’s Manual
VectorCalc User’s Manual
1.0
Introduction
k̂
VectorCalc is a Palm-hosted program that
performs several different vector
calculations. It is comprised of three
different forms that display different
calculated values. Table 1.1-1 shows in
which form each calculation appears.
Form
One
Calculation
Requires
Input
A and/or B
Magnitude of either A
or B
Unit vector of either A A and/or B
or B
Two
Angle between A and A and B
B
Distance between A
A and B
and B
Dot product of A and
A and B
B
Cross product of A
A and B
and B
A±B
Sum of A and B
A and B
Difference between A A and B
and B
Table 1.1-1 Calculations Performed in
VectorCalc
A vector in three-dimensional space is
represented as a directed line segment, has
a magnitude and a direction, and is
composed of three separate components
along the axes that define the threedimensional space (known most commonly
as either x, y, and z or i, j, and k). A vector
r
A can be represented in several different
ways, two of which are ( a1 , a 2 , a3 ) , or
(a1iˆ + a 2 ˆj + a3 kˆ) .
Figure 1.1-1 shows a vector in threedimensional space and its decomposition
along the three axes.
Copyright © 2004 Multiology, LLC
r
A
a
3
ĵ
a
2
iˆ
a
1
Figure 1.1-1. Vector in three-dimensional
space
r
The magnitude of a vector, A , is a scalar
that represents the vector’s length, given by
r
2
2
2
A = a1 + a 2 + a3 , where the small
a’s are the vector components.
A unit vector is a vector with a length of one
in the direction of the original vector, and it is
the original vector divided by its magnitude:
r
ˆA = Ar .
A
The sum of two vectors is a vector whose
result is the addition of the individual
components of the two vectors:
r r
A + B = (a1 + b1 )iˆ + (a 2 + b2 ) ˆj + (a3 + b3 )kˆ
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