Another example: take a right cylinder. Every tangent plane to the cylinder is parallel to the cylinder"s axis.
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Think in the floor of your room together the gray aircraft and think in the wall of your room as the blue plane. The blue line will certainly be the line in between the wall surface in front of the wall surface blue and the ceiling.
A very simple example is two various planes containing the same line: both space parallel to that line and also to any kind of other heat parallel come it.
If you take any type of two intersecting planes they will both be parallel to the line created by their intersection, however they can"t it is in parallel to each other because they intersect.
In the image over both planes are parallel to the line characterized by points A and also B.
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Because in three-dimensional space, the plane that are anchored to a heat still have one more degree the freedom. They deserve to rotate around the line. Therefore the two planes that space parallel to the very same line can be in ~ an infinite variety of angles to every other.
Making lines parallel in 3D is simpler than make planes parallel, due to the fact that planes have extra dimension. You can think that a airplane as an intersection of 2 lines.
So together you can see there is one more line involved. Omitting the extra line is what makes your explain incomplete. No necessarily false. It might still it is in true in one instance out the infinity.
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If you had actually two lines cross each various other (not have to at the right angle) and also you had two planes that were parallel to both of the lines, then you can guarantee the the 2 planes space parallel, since then you would have anchored both the the plane"s dimensions, not just one.