Chapter 9: Vector Calculus
Section 9.2: Vector Objects
Example 9.2.6
The vertices of a triangle are A:1,2, B:4,7, C:3,9. Draw the triangle with sides as vectors from A to B, B to C, and C to A.
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 points A, B, C as free vectors
Context Panel: Assign to a Name≻A
1,2→assign to a nameA
Context Panel: Assign to a Name≻B
4,7→assign to a nameB
Context Panel: Assign to a Name≻C
3,9→assign to a nameC
Define the rooted vectors AB, BC, CA
Write the appropriate difference of two free vectors. Context Panel: Evaluate and Display Inline
Context Panel: Student Vector Calculus≻Conversions≻To Rooted Vector (Enter the root point as a list of coordinates, as per the figure to the right.)
Context Panel: Assign to a Name≻AB, BC, CA, as appropriate
B−A = →to rooted Vector35→assign to a nameAB
C−B = →to rooted Vector−12→assign to a nameBC
A−C = →to rooted Vector−2−7→assign to a nameCA
Obtain a graph of the edges of the triangle
Write a sequence of names of the rooted vectors. Context Panel: Evaluate and Display Inline
Context Panel: Plots≻Arrows
AB,BC,CA = →plot arrows
The initial graph can be morphed into the version below by a series of interactive manipulations via the Context Panel.
Apply Constrained Scaling.
Select arrow AB. Select Style≻Polygon Select Color to change the color of the body of the arrow to red. Repeat for arrow CA. Leave BC black.
Select Axes≻Properties to reset the view. Uncheck "Use data extents" and reset the minimum and maximum values of the range. Click "Apply" to apply the change. Repeat for the Vertical axis.
Maple Solution - Coded
Install the Student VectorCalculus package and execute the BasisFormat command.
withStudent:-VectorCalculus:BasisFormatfalse:
Define the points A, B, C as free vectors.
A,B,C≔1,2,4,7,3,9:
Apply the RootedVector command.
AB≔RootedVectorroot=A,B−A:BC≔RootedVectorroot=B,C−B:CA≔RootedVectorroot=C,A−C:AB,BC,CA
Apply the PlotVector command
<< Previous Example Section 9.2 Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2024. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document
