Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Angle between planes

In the answer that I have, they have taken the normal vector from the 2 planes which I'm ok with and did the dot product with that to find the angle, I'm also ok with this...but then isn't that the angle between the two normal vectors? It says that this is the angle between the two planes. Can someone please explain this to me. Thanks.

Well it really depends what angle you're talking about; when the planes intersect there will be an acute angle and an obtuse angle. The angles between their normals will be the same two angles; conventionally you take the acute angle (but it really doesn't matter).

OP

Thanks for the reply. I'm still not sure what you mean by the same two angles. I have attached a (badly drawn) picture to make this a bit clearer. When the two planes intersect there are angles alpha and theta, suppose angle alpha is the acute angle, you are saying that this is the same as angle x in the picture?

(edited 13 years ago)

Untitled.png4.0KB

Original post by JBKProductions

Thanks for the reply. I'm still not sure what you mean by the same two angles. I have attached a (badly drawn) picture to make this a bit clearer. When the two planes intersect there are angles alpha and theta, suppose angle alpha is the acute angle, you are saying that this is the same as angle x in the picture?

Yup, in that picture

\alpha = x

. Look what happens when

\alpha

becomes really small, for example. Or when

\alpha \to \frac{\pi}{2}

, or

\alpha \to \pi

. You'll see that

x

does the same. [I mean, this doesn't prove that it's true, but it should serve to convince you!]

For what it's worth, by "the two angles" I meant

\alpha

and

\theta

. Then

\alpha = x

and

\theta =

the other angle that the normals meet at (which isn't on your diagram because you didn't carry the normals on past their point of intersection).

(edited 13 years ago)

OP

Thank you! :biggrin:

:biggrin:

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