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Chapter 1: Vectors, Lines and Planes
Section 1.1: Cartesian Coordinates and Vectors
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Example 1.1.4
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Determine the angle that the position vector to makes with the -axis.
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Solution
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Mathematical Solution
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From Figure 1.1.4(a), a graph of the given position vector, the angle is determined by simple right-triangle trigonometry.
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radians or
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use plots, Student:-VectorCalculus in
module()
local p1,p2,p3,p4;
p1:=PlotVector(<1,2>,color=black);
p2:=plot([[[0,0],[1,0]],[[1,0],[1,2]]],style=line,linestyle=dot,color=red):
p3:=textplot({[.5,.1,1],[.9,1,2],[.2,.1,typeset(theta)],[.55,.75,typeset(sqrt(5))]});
p4:=display(p1,p2,p3,scaling=constrained,axes=none);
print(p4);
end module:
end use:
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Figure 1.1.4(a) Right triangle formed by the given position vector and the horizontal
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Maple Solution - Interactive
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The Student MultivariateCalculus package provides the Angle command, which returns (in radians) the angle between two vectors. Use the Context Panel to apply this command to the given position vector and another position vector whose direction is that of the -axis.
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Tools≻Load Package: Student Multivariate Calculus
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Loading Student:-MultivariateCalculus
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Form a sequence of two vectors (see Table 1.1.1), one the given position vector, and the other any position vector whose direction is that of the -axis.
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Context Panel: Evaluate and Display Inline
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Context Menu: Student Multivariate Calculus≻Lines & Planes≻Angle
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Maple Solution - Coded
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Apply the Angle command in the Student MultivariateCalculus package to the given position vector and any other vector whose direction is that of the -axis.
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Install the Student MultivariateCalculus package.
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Apply the Angle command.
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