Chapter 9: Vector Calculus
Section 9.2: Vector Objects
Example 9.2.7
At the point x,y,z=1,2,1, evaluate the vector field F=y z i+x z j+x y k and the free vector V whose components are the same as those of F. On the same set of axes, draw both resulting vectors.
Solution
Maple Solution - Interactive
Initialize
Tools≻Load Package: Student Vector Calculus
Loading Student:-VectorCalculus
Tools≻Tasks≻Browse: Calculus - Vector≻ Vector Algebra and Settings≻ Display Format for Vectors
Press the Access Settings button and select "Display as Column Vector"
Display Format for Vectors
Define the free vector V
Context Panel: Assign to a Name≻V
y z,x z,x y→assign to a nameV
Define the vector field F
Write the name V. Context Panel: Evaluate and Display Inline
Context Panel: Assign to a Name≻F
V = yzxzxy→to Vector Fieldyzxzxy→assign to a nameF
Evaluate the vector field at a point
Write the name F. Context Panel: Evaluate and Display Inline
Context Panel: Student Vector Calculus≻Evaluate≻Complete the dialog as shown below:
Context Panel: Assign to a Name≻FP
F = →evalVF →assign to a nameFP
Write the name FP. Context Panel: Evaluate and Display Inline
Context Panel: Student Vector Calculus≻Queries≻About
FP = →about
Evaluate the free vector at a point
Context Panel: Evaluate at a Point≻x=1,y=2,z=3
Context Panel: Assign to a Name≻VP
V = →evaluate at point →assign to a nameVP
Write the name VP. Context Panel: Evaluate and Display Inline
VP = →about
Graph the vectors resulting from evaluation
Write the sequence of names FP, VP. Context Panel: Evaluate and Display Inline
Context Panel: Plots≻Arrows
FP,VP = →plot arrows
Maple Solution - Coded
Install the Student VectorCalculus package and execute the BasisFormat command.
withStudent:-VectorCalculus:BasisFormatfalse:
Define F and V
Invoke the VectorField command.
F≔VectorFieldy z,x z,x y:
Use angle brackets (inequality symbols) or the Vector command.
V≔y z,x z, x y:
Evaluate at a point
Use the evalVF command to evaluate the vector field at a point.
Use the eval command to evaluate the free vector at a point.
Use the About command to display the characteristics of each vector resulting from evaluation.
FP≔evalVFF,1,2,1
AboutFP =
VP≔evalV,x=1,y=2,z=1
AboutVP =
Use the PlotVector command to obtain a graph of the two arrows produced by evaluating the vector field and the free vector at a point.
PlotVectorFP,VP,color=red,green,labels=x,y,z,scaling=constrained,orientation=−40,75,0,tickmarks=3,3,3
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