Answer only one of the following two alternatives. EITHER The points A, B and C have position vectors i, 2j and 4k respectively, relative to an origin O. The point N is the foot of the perpendicular from O to the plane ABC. The point P on the line-segment ON is such that OP = ¼ON. The line AP meets the plane OBC at Q. Find a vector perpendicular to the plane ABC and show that the length of ON is 4/√(21). Find the position vector of the point Q. Show that the acute angle between the planes ABC and ABQ is cos⁻¹(⅓). OR The curve C has polar equation r = a(1 − cos θ) for 0 ≤ θ < 2π. Sketch C. Find the area of the region enclosed by the arc of C for which ¼π < θ < ¾π, the half-line θ = ¼π and the half-line θ = ¾π. Show that (ds/dθ)² = 4a² sin²(½θ), where s denotes arc length, and find the length of the arc of C for which ¼π < θ < ¾π.