Chapter 1: Vectors, Lines and Planes
Section 1.1: Cartesian Coordinates and Vectors
Example 1.1.10
Determine the coordinates of the tip of the position vector to 1,2,3 if it is translated so its tail is at the point 3,2,1.
Solution
The translate of the given position vector is shown in black in Figure 1.1.10(a).
The green vector is the position vector corresponding to the point 3,2,1.
The three blue vectors indicate the three components, namely, 1,2,3, respectively, of the given position vector.
From Figure 1.1.10(a) and the solution in Example 1.1.9, the coordinates of the tip of the translate of the given position vector are
1+3,2+2,3+1=4,4,4
use plots, Student:-VectorCalculus, plottools in module() local V1,V2,V3,V4,V5,p1,p2,p3,p4,p5,q,X,XX,Y; V1:=RootedVector(root=[3,2,1],<1,2,3>): V2:=<3,2,1>; V3:=RootedVector(root=[3,2,1],<1,0,0>); V4:=RootedVector(root=[3,2,1],<0,2,0>); V5:=RootedVector(root=[3,2,1],<0,0,3>); p1:=PlotVector([V1,V2,V3,V4,V5],color=[black,green,blue$3],width=.1); q:=plot3d(0,x=0..4,y=0..4,grid=[5,5],style=wireframe,color=black): X:=rotate(q,-Pi/2,0,0): XX:=translate(X,0,4,0): Y:=rotate(q,0,Pi/2,0): p2:=display(q,XX,Y); p3:=spacecurve([[3,2,1],[3,2,0]],numpoints=2,color=red,linestyle=dot); p4:=spacecurve([[3,2,1],[0,2,1]],numpoints=2,color=red,linestyle=dot); p5:=display(p1,p2,p3,p4,scaling=constrained,labels=[x,y,z],axes=frame,orientation=[-50,75,0],lightmodel=none,glossiness=0); print(p5); end module: end use:
Figure 1.1.10(a) Translated position vector
Rotating the graph in Figure 1.1.10(a) with the mouse helps clarify the relationships between the vectors in the figure. This example should suggest that "vector addition" (to be discussed in Section 1.2) might provide an algorithmic way to obtain what has been extracted from a graph.
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