MATH 126 Final: MATH 126 UW Final Exam Spring 2011 Solutions

• School: UW
• Department: Mathematics
• Course: MATH 126
• Professor: All

Document Summary

Math 126 final exam hints and answers. Spring 2011: hint: let ~n1 = h 1, 1, 4i and ~n2 = h1, 3, 2i, normal vectors for the two planes. A direction vector for the line of intersection is ~v = ~n1 ~n2 = h14, 6, 2i. To nd a point on the line, you may assume, for instance, that the line intersects the xy-plane and nd the point on both planes with z-coordinate 0: ( 18, 11, 0). Answer: (other answers are possible) x = 18 + 14t, y = 11 + 6t, z = 2t (a) answer: ( ) = 1 + a2 (b) answer: a = 9. 3. (a) answer: z = y + 1. So, a normal vector of the tangent plane is. This must be parallel to h3, 18, 1i. (b) hint: 300 xy: hint: since xyz = 100, z = The only critical point is (2 3 75, 3 75).