I have spent about ten hours on the following problem and I guess it is time to ask for help!
It is known that for any given triangle T in space there is a plane such that the projection of T onto this plane is an equilateral triangle. I want to find the normal vector of this plane given the coordinates of the vertices of T, or vectors that form T (sides of T as vectors), or vectors formed by connecting the origin to vertices, or............... I want an explicit and nice solution. I can come up with an ugly expression but I want something elegant. (I haven't seen this in a book but intuitively one is inclined toward the assumption that an elegant solution must exist, perhaps by representing T in a novel and non-standard way). Many Thanks in advance, Ali
