Chapter 9: Vector Calculus
Section 9.2: Vector Objects
Example 9.2.4
Draw the surface z=x2y2, and on it, the coordinate curves x=1/2 and y= −1. Along these coordinate curves, draw tangent, principal normal, and binormal vectors.
Solution
Initialize
Install the Student VectorCalculus package and execute the BasisFormat command.
withStudent:-VectorCalculus:BasisFormatfalse:
Define R
Apply the PositionVector command.
R≔PositionVectorx,y,x2y2
Use the PlotPositionVector command to obtain the required graph
PlotPositionVectorR,x=−1..1,y=−1..1,coordcurve=x=1/2,tangent=true,normal=true,binormal=true,vectornum=2,tangentoptions=color=red,y=−1,tangent=true,vectornum=2,scaling=constrained,axes=frame,labels=x,y,z,orientation=−35,60,0,tickmarks=3,3,3
Note the use of the coordcurve option for graphing coordinate curves. The tangent, normal, and binormal options cause those vectors to be drawn. The vectornum commands controls the number of vectors to draw along the coordinate curve. Color is applied to the tangent vectors along the curve x=1/2 via the tangentoptions option.
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 9.2.4(a) where the About command is applied to verify the properties of the object.
Interactive definition of a position vector
Write a free vector. Context Panel: Evaluate and Display Inline
Context Panel: Student Vector Calculus≻Conversions≻To Position Vector
Context Panel: Student Vector Calculus≻Queries≻About
x,y,x2y2 = →to position Vector →about
Table 9.2.4(a) Interactive construction of a position vector
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