In an exercise I was asked to find a formula of the form $F(x,y,z)=C$ for a cylinder though the axis $(t,t,t)$ and radius $R$. The formula I got seemed a bit suspicious so I wanted to ask if I have it right.
Basically I used the vector formula for the distance between a line and a point found here: http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html. I chose $x_1=(0,0,0), x_2=(1,1,1)$ to determine the line. Marking $r=(x,y,z)$ for a point on the cylinder, after some simplification and moving things around in the equation, I got that each point on the cylinder needs to fulfill the formula:
Have I correctly derived the formula?
Thanks a bunch!