1. The problem statement, all variables and given/known data Show that the circle that is the intersection of the plane x + y + z = 0 and the sphere x2 + y2 + z2 = 1 can be expressed as: x(t) = [cos(t)-sqrt(3)sin(t)]/sqrt(6) y(t) = [cos(t)+sqrt(3)sin(t)]/sqrt(6) z(t) = -[2cos(t)]/sqrt(6) 2. Relevant equations 3. The attempt at a solution At first, I tried to let z=-x-y then sub it into the equation of the sphere: x2+y2+(-x-y)2=1 x2+y2+x2+2xy+y2=1 2x2+2xy+2y2 = 1 And i stuck at here, I can't make it into a circle equation. So, I changed another way. I equated two equations, so it becomes: x2 + y2 + z2 -1 = x+y+z x2+ x + y2 + y + z2 +Z -1 =0 (x-1/2)2 + (y-1/2)2 + (z-1/2)2 = 7/4 *By completing the square But isn't this is an equation of a sphere?? Shouldn't it just a circle? Any help is appreciated!