Chapter 1: Vectors, Lines and Planes
Section 1.2: Vector Arithmetic
Obtain PQ→, the vector from P:2,3 to Q:−5,1, then draw it and the position vectors to points P and Q.
In Figure 1.2.9(a), the red and green arrows represent the position vectors to points P and Q, respectively.
The black arrow, PQ→, the vector from point P to point Q, is the requisite vector.
The gray vector, PQ→#, is the translation of PQ→ back to the origin.
Vector addition gives PQ→′+P=Q, so PQ→# = Q−P.
Translating PQ→# yields PQ→, the vector from point P to point Q.
Figure 1.2.9(a) Vectors P, Q, and PQ→
Maple Solution - Interactive
Enter the data
Enter position vector as per Table 1.1.1.
Context Panel: Assign to a Name≻P
2,3→assign to a nameP
Context Panel: Assign to a Name≻Q
−5,1→assign to a nameQ
Write the difference of position vectors Q and P.
Context Panel: Evaluate and Display Inline
Q−P = −7−2
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.
Type P, Q, and Q−P, as appropriate, and press the Enter key
Context Panel: Plots≻Arrow from origin (for P and Q)
Context Panel: Plots≻Arrow from point (for Q−P)≻2,3
Copy/paste each arrow.
Context Panel: Color
Maple Solution - Coded
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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