Solving for k in 3D Plane Intersection at 60 Degrees

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Homework Help Overview

The problem involves determining the value of k in the equation of a plane, given that it intersects another plane at an angle of 60 degrees. The subject area relates to geometry in three-dimensional space, specifically focusing on the properties of planes and angles between them.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss finding the angle between two vectors, suggesting that the normal vectors of the planes could be used to determine the angle between the planes. There is mention of using the dot product to find the cosine of the angle between these normals.

Discussion Status

The discussion is ongoing, with some participants providing guidance on how to approach the problem by identifying normal vectors and using the dot product. However, there is no explicit consensus on the steps to take, and one participant expresses concern about the nature of the assistance being provided.

Contextual Notes

There is an indication that the original poster has not yet responded to the suggestions, leaving the discussion open-ended. Additionally, there may be specific requirements from the teacher regarding the proof of the relationship between the angles of planes and their normals.

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Homework Statement


Given the plane x + ky + 2z - 9 = 0, find k if the plane makes an angle of 60 degrees with the plane 2x + 2y - z = 0.


Homework Equations





The Attempt at a Solution


I'm stumped on this question. No idea of even how to start this one.
 
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can you find the angle between two vectors?
 
First find the normal vector for each plane- that should be easy. Then use the dot product to find the cosine of those two vectors.
 
as hallsofIvy mentioned, the angle between two planes is the angle between their normals. Using the dot product will give you the answer,

BUT

your teacher might require you to actually prove that the angle between two planes is the angle between their normals. to prove this, just study the quadrilateral formed by the two planes and the two normals.
 
Just wondering... Are we now just giving out the solutions? We haven't even heard back from the OP.
 

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