Vector Calculus · Superchallenge problem

Let $C$ be the circle in which the plane $x + y + z = 0$ cuts the sphere $x^2 + y^2 + z^2 = 1$. Evaluate the scalar line integral $\displaystyle\int_C (x + 2y + 3z)^2\,ds$. Give your answer in terms of $\pi$.