Solving for k in 3D Plane Intersection at 60 Degrees

[kevykevy]

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.

 

[robphy]

can you find the angle between two vectors?

 

[HallsofIvy]

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.

 

[Tom1992]

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.

 

[robphy]

Just wondering... Are we now just giving out the solutions? We haven't even heard back from the OP.