Chapter 1: Vectors, Lines and Planes
Section 1.2: Vector Arithmetic
Example 1.2.9
Obtain PQ→, the vector from P:2,3 to Q:−5,1, then draw it and the position vectors to points P and Q.
Solution
Mathematical Solution
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→
PQ→=Q−P=−51−23=−7−2
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
Obtain PQ→
Write the difference of position vectors Q and P.
Context Panel: Evaluate and Display Inline
Q−P =
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. Select arrow
Context Panel: Color
P
→plot arrow
Q
Q−P
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.
P≔2,3:Q≔−5,1:PQ≔VectorCalculus:-RootedVectorroot=2,3,Q−P:VectorCalculus:-PlotVectorP,Q,PQ,color=red,green,black,width=.2,scaling=constrained
<< Previous Example Section 1.2 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