The cross product has many important uses in mathematics. Among the more useful, particularly in this class, is that the cross product of two vectors gives us an \"oriented area.\" Here is what we mean by this. Suppose P is a parallelogram with sides a and b. The cross product a X b has both magnitude and direction. The magnitude of a X b provides us with the area of P; this you can verify (see book or Exercise 15). The direction of a X b provides us with an orientation for P as follows. If we were to stand on the parallelogram P, we might want to know if we were standing on the \"top\" or on the \"bottom\" of P with respect to a X b. Since a X b is a vector that is perpendicular to both a and b, the cross product a X b is either in the same direction as the vector from our feet to our head or it is in the opposite direction. If it is in the same direction, then we are standing on \"top\" of P with respect to a X b, otherwise we are standing on the \"bottom\" of P with respect to a X b. Most of the following are modied versions of exercises from Stewart's Muirivariable Calculus. 22. (12.3, 12.4, and 12.5) Suppose P is the plane described by the equation as: + by + 02 + d = 0. Given two points (30, yo, 20) and (9:1, yl, 21), how does one go about determining whether or not the two points lie on the same side of the plane. Carefully explain your reasoning. [Advice: This is strongly, but not directly, related to the paragraph at the top of this homework]