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Unformatted text preview: MAT235CALCULUS II, FALL 2010 ASSIGNMENT #2, Solutions Problem 1 Identify and sketch the quadric surface consisting of all points ( x,y,z ) with x y 2 +2 y + z 2 = 2. Justify your answer carefully. It is recommended that you try to sketch with pencil so that you can improve your sketch. Scanned solution is posted onto the next file Problem 2 Let A,B,C,D be four points in R 3 which are not necessarily coplanar. Let M be the midpoint of the segment AC , and N be the midpoint of the segment BD . If MB  MD = NA  NC, show that  AC  =  BD  . Hint: Observe that AC = NC NA, and BD = MD MB. (1) Also show that 2 MN = MB + MD, 2 NM = NA + NC . Explain why the last two relations imply that  MB + MD  =  NA + NC  (2) Use (1), (2) and the assumption of the exercise to show the desired result. The identity  a  2 = a  a is useful. Solution : We have MN = MB + BN, (3) and MN = MD + DN. (4) Since BN = DN (because N is the midpoint of BD), by adding equations (3) and (4) we obtain that 2 MN = MB + MD. Similarly, we obtain that 2 NM = NA + NC. (5) The last two relations give that ( MB + MD ) 2 = ( NA + NC ) 2 (here by the square we mean...
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This note was uploaded on 12/05/2010 for the course MAT mat235 taught by Professor Jung during the Fall '10 term at University of Toronto Toronto.
 Fall '10
 JUNG
 Calculus

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