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Chapter 1: Vectors, Lines and Planes
Section 1.2: Vector Arithmetic
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Example 1.2.7
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Draw the parallelogram of addition for the sum of and .
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Solution
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Mathematical Solution
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The requisite parallelogram of addition is shown in Figure 1.2.7(a).
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There are three (position) vectors whose tails are at the origin. The red arrow represents the vector A; the green, B; and the black, the resultant .
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The translate of A, also in red, has its tail at the tip of B. The translate of B, also in green, has its tail at the tip of A.
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>
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use plots, Student:-LinearAlgebra in
module()
local p1,p2;
Student:-SetColors(red,green,gray,yellow):
p1:=VectorSumPlot(<3,-4>,<2,5>,caption="");
p2:=display(p1,labels=[x,y]);
print(p2);
end module:
end use:
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Figure 1.2.7(a) Parallelogram of addition
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Maple Solution - Interactive
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Table 1.2.7(a) provides a solution via the
task template, itself an implementation of the VectorSumPlot command in the Student LinearAlgebra package. Unfortunately, the default colors are not optimal and are best changed before the task template is used. A command to change these colors is executed when the button in the first sentence of this paragraph is pressed.
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Tools≻Tasks≻Browse: Linear Algebra≻Visualizations≻Vector Sum Plot
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Plot the Sum of Vectors
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Vectors (2 or more):
Sum first
=
Resultant =
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Table 1.2.7(a) The Vector Sum Plot task template
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Maple Solution - Coded
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Executing the following two commands will generate Figure 1.2.7(a).
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