Here is the problem I have for my homework...

Find an equation for the cone in 3D space which has vertex angle 2pi/3. (Hint: What is the vertex angle for z = sqrt(x^2+x^2)? How could you change this equation to get a cone with dierent angle? )

So the work that I have is that I created two vectors that go from the origin along the y-axis. I got the two vectors to be A=i+k and B=-i+k.

The angle between two vectors is A.B=||A|| ||B|| cos(theta)

A.B = -1 and ||A|| ||B|| = sqrt(2)*sqrt(2) = 2

Therefore theta = arccos(-1/2), which is 2pi/3.

First of all, is this correct? And if it is not, what might I be doing wrong, do I have the definition of a vertex angle correct and can I just create vectors like that?

Thanks for your help,

Tyler