2. The distance from (x; y; z) to the origin is d = f(x; y; z) = p x 2 + y 2 + z 2 . We want to minimize this distance d, which is equivalent to minimizing d 2 = (f(x; y; z))2 = x 2 + y 2 + z 2 . (a) Amongst all the points on the plane 2x 3y z = 4, there is a unique point that is closest to the origin. Find this point using Lagrange multipliers, and Önd the distance of this point to the origin. (b) Earlier in the semester, we learned a formula for the distance from a point to a plane. Apply this formula to verify your answer in (a). (c) Amongst all the points on the surface y 2 = 9+kxz, there is a unique point that is closest to the origin for certain set of k 6= 2 values. For which set of k 2 Rn f2g values do we have this point? In other words, Önd all values of k, k 6= 2, for which there is only one point on the surface that attains the minimum distance. Use any method of your choice.