Chapter 1: Vectors, Lines and Planes
Section 1.2: Vector Arithmetic
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Example 1.2.9
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Obtain , the vector from P: to Q:, then draw it and the position vectors to points P and Q.
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Solution
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Mathematical Solution
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In Figure 1.2.9(a), the red and green arrows represent the position vectors to points P and Q, respectively.
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The black arrow, , the vector from point P to point Q, is the requisite vector.
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The gray vector, #, is the translation of back to the origin.
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Vector addition gives , so # = .
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Translating # yields , the vector from point P to point Q.
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Figure 1.2.9(a) Vectors P, Q, and
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Maple Solution - Interactive
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Enter the data
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Context Panel: Assign to a Name≻P
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Context Panel: Assign to a Name≻Q
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Obtain
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Write the difference of position vectors Q and P.
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Context Panel: Evaluate and Display Inline
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=
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Obtaining Figure 1.2.9(a) interactively isn't that difficult. The three main arrows are drawn separately, their colors changed via the Context Panel, and combined via drag-and-drop. Consequently, re-executing this whole document will cause the vectors shown below in red and green to be rendered in black.
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Type P, Q, and , as appropriate, and press the Enter key
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Context Panel: Plots≻Arrow from origin (for P and Q)
Context Panel: Plots≻Arrow from point (for )≻
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Copy/paste each arrow.
Select arrow
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Maple Solution - Coded
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The following sequence of commands will draw the principal vectors in Figure 1.2.9(a). The RootedVector command creates a vector whose "tail" or root is part of the data structure. The PlotVector command makes provision for assigning arbitrary colors to individual vectors.
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