1. Vector Calculus page 77 problem 1
Let P0 , P1 , . . . , Pk1 be the vertices of a regular polygon having k sides. Let O be the center of the polygon.
Show that i=0 OPi = 0.
Remember that adding vectors can be expressed geometrically by plac
1. Vector Calculus page 133 problem 32
Find any planes tangent to the curve z = x2 6x + y 3 that are parallel to the plane 4x 12y + z = 7.
The tangent plane to a curve f : R2 R at a point (a, b) is given by z = f (a, b)+ fx (a, b)(x a)+ fy (a