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The "Intersection" of three non-parallel planes
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The sequence of graphics below illustrates that three non-parallel do not necessarily meet in a point. Each of the planes is illustrated by itself, then the intersection of planes 1 and 3 is shown, followed by the intersection of plane 2 and 3, followed by a graphic showing all three plane together. The three planes meet in pairs in lines, as any three planes would, but in this case, these 3 separate lines are in fact parallel, and so there is not one common point of intersection.
The final two graphics in the sequence illustrate just the lines of intersection, showing, in the final graphic, the triangular prism cut off as the three planes meet in pairs.
Plane 1 : x + 2y - z==4
Plane 2: x + 4y + z==2
Plane 3: y+ z== 6
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% End of Graphics
MathPictureEnd
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