Chapter 9: Vector Calculus
Section 9.2: Vector Objects
Draw the surface z=x2y2, and on it, from the vector field F=y z i+x z j+x y k, normalized vectors and their normal components, at the points corresponding to x,y=1/2,1/2 and −1/2,−1/2.
Install the Student VectorCalculus package and execute the BasisFormat command.
Apply the PositionVector command.
Apply the VectorField command.
F≔VectorFieldy z,x z, x y
Use the PlotPositionVector command, applying the Normalize command to F
The vectorfield option allows the arrows from an arbitrary vector field to be drawn on the surface. The normalfield option causes the command to draw principal normal vectors on the surface. The normalfieldoptions option is used to assign the color black to the normal vectors. The vectorfieldoptions option is used to assign the color gold to the normal components of F. The points option dictates where vectors are to be drawn.
The PositionVector and the VectorField can be formed interactively via the Context Panel, but at this time there is no simplified access to the PlotPositionVector command. See Table 9.2.5(a) where the About command is applied in each case to exhibit 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
→to position Vector
Interactive definition of a vector field
Context Panel: Student Vector Calculus≻Conversions≻To Vector Field
y z,x z,x y =
→to Vector Field
Table 9.2.5(a) Interactive construction of a position vector and a vector field
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