Problem 3. The surface 3 described by z = 3:2 + y2 intersects the plane P with equation 2118 + 4y + 202 : 400 at the point (4, 2, 20). Find the angle of intersection between the tangent plane to the surface at this point and the plane P. Problem 4. The area of a triangle with side lengths (1:, y and z is given by ACE-5:953) : V 8(3 _$)(3 _y)(5 _Z) where 8 : as: + y + z). Show that a triangle with xed perimeter has maximum area when it is an equilateral triangle