I am given:
x^2 + y^2 + z^2 + 2*x*y + 2*x*z - 2*y*z = 1
I need to write this in standard form, and sketch the surface. I used Matlab to give me an idea of what the surface looks like. From what I can gather it is a hyperboloid of one sheet orientated around the vector r (-1,1,1). And this is as far as I got. Any help parameterizing this, or coming up with the Cartesian equation would be much appreciated!