We will concentrate on 2D space for now as shown in Figure 12.
Figure 12. 2D space. |
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VI Info - Figure 12 contains three pictures. The left-most picture shows a vector V extending from A on the left to B on the right. Two short vertical lines of the same length extend upward from A and B and have no label. Short, upward sloping lines extend from the tops of those two lines meeting in the middle. The overall figure resembles an end view of a very simple house with a sloping roof that has its peak in the middle. The entire structure is enclosed near the center of a square border.
The center picture shows the same structure superimposed on a sheet of graph paper with horizontal and vertical grid lines. The structure is in the same location in the square border. Horizontal and vertical axes intersect at an origin near the lower left corner of the square. The origin is labeled (P sub 0). The axes and the resulting grid are parallel to the sides of the square. In this case, the vector V extends from point A at (2,2) to point B at (6,2).
The picture on the right shows the same structure in the same location in the square border superimposed on the same sheet of graph paper. However, in this case, the graph paper has been rotated and possibly moved such that the origin has been moved down and to the right and the axes are no longer parallel to the sides of the square. In this case, the vector V extends from point A at approximately (2,3) to point B, which is at approximately (4.8,1.6).
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