MATH 32A Final: MATH32A Final Exam 2014 Winter
Document Summary
Instructions: do not open this exam until instructed to do so. You will have 3 hours to complete the exam. Please print your name and student id number above. You may not use calculators, books, notes, or any other material to help you. Please make sure your phone is silenced and stowed where you cannot see it. You may use any available space on the exam for scratch work. If you need more scratch paper, please ask one of the proctors. You must show your work to receive credit. 6x + 9y 2z = 2. (a) (1 pt) write down a normal vector for the plane: (b) (5 pts) choose any point q in the plane, and compute the projection. Note: the remaining parts of this problem may be done in various orders. Be speci c, and justify your answer: (10 pts) the temperature at each point (x, y, z) in a room is given by.