Chapter 1: Vectors, Lines and Planes
Section 1.1: Cartesian Coordinates and Vectors
Example 1.1.9
Determine the coordinates of the tip of the position vector to 1,2 if it is translated so its tail is at the point 3,−4.
Solution
In Figure 1.1.9(a), the position vector to 1,2 has been translated so its tail is at the point 3,−4.
With the translated vector, the dotted red lines form a right triangle whose legs have the dimensions of the components of the position vector.
Simple arithmetic shows that the coordinates of the tip of the translated vector must be
3+1,−4+2=4,−2
The vector arithmetic discussed in Section 1.2 will reveal that the result suggested by Figure 1.1.9(a) is normally obtained by the addition of vectors.
use plots, Student:-VectorCalculus in module() local V,p1,p2,p3,p4; V:=RootedVector(root=[3,-4],<1,2>): p1:=PlotVector(V,color=black,width=0.033); p2:=plot([[3,-4],[4,-4],[4,-2]],style=line,color=red,linestyle=dot); p3:=textplot({[3,-4.2,typeset(``(3,-4))],[3.5,-3.8,1],[3.9,-3,2]}); p4:=display(p1,p2,p3,scaling=constrained,view=[0..4.5,0..-4.5],labels=[x,y]); print(p4); end module: end use:
Figure 1.1.9(a) Translated position vector
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