Initialize
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Install the Student VectorCalculus package and execute the BasisFormat command.
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Define R
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Use the PlotPositionVector command to obtain the required graph
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The tangent vectors are in black, the principal normal vectors in green, and the vectors representing are in red. The tangent and normal options cause the unit tangent and principal normal vectors to be drawn. The pvdiff option causes derivatives of R to be drawn. Characteristics of the tangent, normal, and second derivative vectors are applied with tangentoptions, normaloptions, and diffoptions, respectively. Location of the tangent and normal vectors is controlled by the points option. Location of the derivative vectors is controlled by the vectornum option. With this number set to 3 in an interval of length , the first and last point are set at half from the endpoints, and the three points themselves are separated by .
The PositionVector can be formed interactively via the Context Panel, but at this time there is no simplified access to the PlotPositionVector command. See Table 9.2.2(a) where the About command is applied to verify the properties of the object.
Interactive definition of a position vector
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Write a free vector.
Context Panel: Evaluate and Display Inline
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Context Panel: Student Vector Calculus≻Conversions≻To Position Vector
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Context Panel: Assign to a Name≻PV
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Write the name PV.
Context Panel: Evaluate and Display Inline
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Context Panel: Student Vector Calculus≻Queries≻About
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Table 9.2.2(a) Interactive construction of a position vector
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