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Unformatted text preview: , , 0) . 32. If this were in the xyplane, it would be a circle of radius 1 centered at the origin. Since it is in R 3 (and z can have any value), it is instead an inFnite cylinder of radius 1 with the zaxis as its axis. 36. 0 ≤ x ≤ 1 , ≤ y ≤ 2 , ≤ z ≤ 3 . 41. In order for a point ( x,y,z ) to be equidistant from both (1 , 5 , 3) and (6 , 2 ,2) , it must satisfy the equation r ( x + 1) 2 + ( y5) 2 + ( z3) 2 = r ( x6) 2 + ( y2) 2 + ( z + 2) 2 . This leads to ( x + 1) 2 + ( y5) 2 + ( z3) 2 = ( x6) 2 + ( y2) 2 + ( z + 2) 2 ( x 2 + 2 x + 1) + ( y 210 y + 25) + ( z 26 z + 9) = ( x 212 x + 36) + ( y 24 y + 4) + ( z 2 + 4 z + 4) 2 x10 y6 z + 35 =12 x4 y + 4 z + 44 14 x6 y10 z = 9 . This is a plane....
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 Spring '08
 Starr
 Math, Distance, Orders of magnitude

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