Originally Posted by

**earboth** Only some hints:

4. A straight line through M perpendicular to p intersects p in the center C of the circle. You should come out with $\displaystyle C \left(\frac13, \frac13, \frac13 \right)$. So the distance of C to M is $\displaystyle d = \frac13 \cdot \sqrt{3}$

5. Use r and d to determine the radius of the circle.

6. A vector $\displaystyle \vec v$ parallel to p is perpendicular to $\displaystyle \vec n$, that means $\displaystyle \langle 1,1,1 \rangle \cdot \vec v = 0$

I'll show you how to get $\displaystyle \vec v$ in general:

$\displaystyle \langle a,b,c \rangle \cdot \vec v = 0~\implies~ \vec v = \langle -b, a, 0 \rangle ~\vee~\vec v = \langle -c, 0, a \rangle ~\vee~\vec v = \langle 0, -c, b \rangle$

7. For the parametrization of the curve C you have to use the sine and cosine function.