Calculate Angles Between Planes in 3D Space

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The discussion revolves around calculating the angles between two planes defined by the equations 2x+y-3z+7=0 and 4x-y+7z+5=0 in 3D space. Participants are exploring the geometric relationships between these planes and their normal vectors.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks guidance on how to begin the problem, specifically regarding the calculation of angles between the planes. Some participants suggest finding the normal vectors of the planes and question the relationship between these vectors and the angles between the planes. Others mention the concept of supplementary angles in this context.

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blimkie
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calculate the angles bewteen of the intersection of the planes:
2x+y-3z+7=0 and 4x-y+7z+5=0

any takers? i just need an idea of where to start

thanks
 
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Do you know how to find the normal vectors for the two planes?
Do you know how to find the angle between two vectors?

Do you see why the angle between the two vectors is the angle between the planes?
(Oh, and there is only one angle, not "angles".)
 
Well there is always the supplementary angle too of course, but if you have one, the difference between pi and that angle is the other one.
 
Just to add:

[tex]a(x-x_0)+b(y-y_0)+c(z-z_0)=0[/tex]

is the general equation of a plane. The vector <a,b,c> is the normal vector to that plane. Can you see where to get a, b, and c from your original planes?

Alex
 

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