(1) Find an equation of a plane, II, such that is has the following properties:

(a) The minimum distance from the point (7, -3, 2) to II is equal to the minimum distance from the point (7, 3, -1) to II.

(b) The plane, II, does not contain either of the points (7, -3, 2) or (7, 3, -1).

(c) The plane, II, contains the point (12, 1, 2.5).

(d) The plane, II, is not parallel to the yz-plane.

(2) The curve defined by the vector valued function,r(t) = {4 cos(t), sqrt(32) sin(t), 4 cos(2t)},can be viewed as "living", or existing, on a quadratic surface. What is an equation of a quadratic surface that r(t) lives on? What is the name of this type of quadratic surface?

(3) Show that the planeax + by + cz = dand the liner(t) = r + tv,not in the plane, have no points of intersection if and only ifv (dot product) {a,b,c}=0. Give a geometric explanation of the result.

I don't expect you guys/gals to do all my work but I'm having trouble finding a starting approach to any of these problems. Any hints would be greatly appreciated. Thank you so much!