- Thread starter RONY1
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Such angles are

Can you quote the definition you were given, so I can see how you might be misreading it?

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Well is really simpler than that. The angle between two planes is the angle between their normals.Angle between 2 planes. We are taught to locate such an angle with 2 vertices that descend towards the intersection of the planes and the vertex of it. But what is the geometric proof that all the angles we create like this are the same ?!

Given \(\Pi_1: P+t\cdot \vec{N_1}~\&~\Pi_2: P+t\cdot \vec{N_2}\), then the angle between the planes is the angle between \(\vec{N_1}~\&~\vec{N_2}\)

Now to answer your question, that angle does not change because the normals are fixed.

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No you explained yourself. You just do not know or don't understand the definition.

The angle between two intersecting planes is the angle between there normals. that is the definition

Example :\(\Pi_1: x-2y+5z=10~\&~\Pi_2: 2x+5y-z=15\) are two planes.

The two normals are \(N_1: <1,-2,5>~\&~N_2: <2,5,-1>\).

The angle between them is \(\arccos\left(\dfrac{N_1\cdot N_2}{\|N_1\|\cdot\|N_2\|}\right)\).

By looking at your own diagram that can be seen.

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And I asked for the definition you were given, to see whether it actually says what you say it does. Your picture here seems to show right angles, which as I said are required if you make this kind of definition; is that part of your definition, or not?

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If they formed different angles with the line, rather than merely being located in different places, then this would not be true.

In particular, imagine that the same 2-plane intersection line also uses 2 similar planes, let's say adjacent, but the angle between them is a bit different ...

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This is easy to prove, if it were two angles on the same plane (simple geometry)

In my language, there is no such book, nor paper / plain and digital ...

The above space geometry is neglected in my country's methodology

But two lines that share a point, define a plane. Just work in that plane. No need to bother with space or any other plane.

This is easy to prove, if it were two angles on the same plane (simple geometry)

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