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If two planes are intersected by making a straight line, like $AB$ then

Does the angle between two planes (see figure) always given by the angle between normal vectors ($n_1$ and $n_2$) ?

enter image description here

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3 Answers 3

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Yes, it is. ${}{}{}{}{}{}{}{}$

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Yes. See here

It[The angle between two planes] is defined as the angle between 2 lines, one in each plane, so that they are at right angles to the line of intersection of the 2 planes (like the angle between the tops of the pages of an open book).

To find this angle, will we first have to find the equation of the line of intersection of the 2 planes, and then find 2 vectors which are in the planes and perpendicular to this? Fortunately no! We just need to know a normal vector to each of the planes.

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In your figure, thing is right. If you reverse vector n1, the angle between two planes plus that between two normal vectors will be 2pi. There will be some difference.

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  • $\begingroup$ Huh? I'm not sure what you're trying to say here $\endgroup$
    – SSumner
    Mar 29, 2013 at 16:02
  • $\begingroup$ @SSumner: The point must be that the two planes divide space into four regions with one angle in each. Two of the angles equals the angle between the normals, the two others are its supplementary angle. $\endgroup$ Mar 29, 2013 at 22:13
  • $\begingroup$ Ah, okay. I understand. Could be worded clearer in my opinion $\endgroup$
    – SSumner
    Mar 29, 2013 at 22:45

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