# $2$ planes and angle between them

IF I have two $3d$ planes such as Oab and Oa'b'. If these two planes intersect a horizontal plane and the intersection of each plane makes AB and A'B' lines. then,

1. Does the angle between AB, A'B' i.e. APA' is equal to the angle between normal vectors (i.e. n1 and n2) of the planes?

2. Does this scenario is always true, even if we intersect these two planes with third plane which is not horizotal (i.e. instead of XY , if there is oblique plane)?

Please, answer my both questions.

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## 1 Answer

It is not, in general, true that the angle between the normal vectors $n_1$ and $n_2$ of two planes is equal to the angle between the lines of intersection $AB$ and $A′B′$ of these two planes with a third plane.

For example, you may have two non-parallel planes which intersect the XY plane in parallel lines.

Also, there is nothing special about the XX-plane being 'horizontal'.

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thanks, but answer is not clear to me. –  gnp Mar 28 '13 at 10:14
Which part of the answer do you not understand? –  Eckhard Mar 28 '13 at 10:15
according Q1, you clearly did not say that ang. between n1, n2 is equal the angle between AB, A'B'. –  gnp Mar 28 '13 at 10:44
@gnp: I said that the angle between $n_1$ and $n_2$ is NOT, in general, equal to the angle between the lines $AB$ and $A'B'$. The answer to Q1 is therefore 'no'. The answer to Q2 is also 'no'. –  Eckhard Mar 28 '13 at 10:48
ok, I got now. I think I made a small mistake and I should say not n1 and n2. But XY projection of n1 and n2. According to my update, does my Q1 give "yes" ? –  gnp Mar 28 '13 at 10:54