1. The problem statement, all variables and given/known data Parameterise the circle whose diameter is the line joining (1,0,0) and (0,0,1) and which lies in the plane x+y+z=1 2. Relevant equations 1. Let N be a unit normal vector for the plane. 2. Let C be the circle center, and let R be the radius. 3. Let U be a unit vector from C toward a point on the circle. 4. Let V = N x U. 5. Let t be the parameter. 6. A point P is on the circle if... P = C + R cos(t) U + R sin(t) V 3. The attempt at a solution This is the first time I am solving this sort of question. By following the procedure, I have N=1/sqrt3(1,1,1), C=(1/2,0,1/2), U=1/sqrt2(1/2,0,-1/2) (from C to (1,0,0)), V=0.5/sqrt6(-1,2,-1) (vector product with N and U). R=1/sqrt2. I'm not sure whether these values are right.