Chapter 1: Vectors, Lines and Planes
Section 1.1: Cartesian Coordinates and Vectors
Example 1.1.7
Draw the position vector to 1,2,3 translated to the point 2,2,−3.
Solution
Interactive Solution
Figure 1.1.7(b), showing the position vector to 1,2,3 translated so its tail is at the point 2,2,−3, is obtained interactively as follows.
As per Table 1.1.1, construct the position vector to 1,2,3 and press the Enter key.
Context Panel: Plots≻Arrow from point Fill in the "Specify arrow length and base point" dialog as per Figure 1.1.7(a) and click OK.
plots:-arrow([2,2,-3],convert(<1,2,3>,'list'),'length'=sqrt(14),'scaling'='constrained');
Figure 1.1.7(b) Translated position vector
Figure 1.1.7(a) "Specify arrow length and base point" dialog
Coded Solution
The VectorCalculus packages provide the construct of the "rooted vector", allowing for the definition of a vector whose "tail" is fixed at a specified "root point." As stated earlier, the PlotVector command is the most convenient command for graphing vectors of all types.
Tools≻Load Package: Student Vector Calculus
Loading Student:-VectorCalculus
Apply the RootedVector command and press the Enter key.
V≔RootedVectorroot=2,2,−3,1,2,3
Apply the PlotVector command, and press the Enter key.
PlotVectorV,scaling=constrained
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