Unformatted text preview: xyplane “straight up” (or down). Note the standing convention that, when we draw pictures of space, we regard the xaxis as pointing toward us (or slightly to our left) out of the page, the yaxis as pointing to the right in the page, and the zaxis as pointing up in the page (Figure 1.4 ). This leads to the identi±cation of the set R 3 of triples ( x,y,z ) of real numbers with the points of space, which we sometimes refer to as three dimensional space (or 3space ). As in the plane, the distance between two points P ( x 1 ,y 1 ,z 1 ) and Q ( x 2 ,y 2 ,z 2 ) in R 3 can be calculated by applying Pythagoras’ Theorem to the right triangle PQR , where R ( x 2 ,y 2 ,z 1 ) shares its last coordinate with P and its other coordinates with Q . Details are left to you (Exercise 12 ); the resulting formula is  PQ  = r △ x 2 + △ y 2 + △ z 2 = r ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 . (1.2)...
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 Fall '08
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 Calculus, Vectors, Cartesian Coordinate System, Horizontal plane, xy plane, Pxy

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