1. (1 point) Find an example of u, v, w E R* to show that the cross product is not associative (i.e., find an instance where (u x v) x w / ux (v x w)). 2. (6 points) (a) Find an equation of the plane that passes through (3, 2, 1), (1, 2,3) and (9, 5, 4). (b) Find a line in the plane a + y + z = 3 that is perpendicular to the line with parametric form (t - 2, t/3, 13 - 4t). Hint: Find the intersection between the given line and plane first. (c) Find a parametric form of the line that passes through the (2, -1, 2) and is perpen- dicular to the line with parametric form (t, 2t, t). (Recall that to be perpendicular, lines must intersect.) (d) Find an equation of the plane that passes through (2, 7, 2) and is perpendicular to the line with parametric form (1 - 2t, t, -3t + 12). (e) Find an equation of the plane that goes through the point (1, 0, 2) and contains the intersection of the planes x - y - z = 1 and y + z = 3. (f) Find the distance from (2, -7, -1) to the plane x - 5y + 22 = 1 3. (1 point) Find a parametric representation for the intersection of the surface x2 + 4y? = 4 with the plane 2y + z = 4. 4. (2 points) Consider two curves in space parametrizations: r(t) = (t, +3, +2) q(t) = (3 - t, cos( at), t/2) (a) Find a point of intersection of these 2 curves. (b) Find an equation of the plane tangent to both curves at the point of intersection from part (4a)