(a) Show that the lines r1(t) = (2, 1, 4) + t(1, 1, 1) and r2(s) = (1, 0, 0) + s(0, 1, 2) are skew. [3 points]

(b) The two lines in (a) lie in parallel planes. Find equations for these two planes. Express your answer in the form ax + by + cz + d = 0. [Hint: The two planes will share a normal vector n. How would one find n?] [3 points]

(c) Find the shortest distance between the two lines in (a). [2 points]

(d) The sphere x^2 4x + y^2 4y + z^2 + 8 = 3/2 lies on one side of the plane containing r1(t) that you have found in part (b). Find its radius and centre. Hence find the shortest distance between it and the plane. [4 points]