Unformatted text preview: determine a line: the slope re±ects the direction (or tilt) of the line, and then the yintercept distinguishes between the various parallel lines with a given slope by specifying a point which must lie on the line. A direction in 3space cannot be determined by a single number, but it is naturally speci²ed by a nonzero vector, so the threedimensional analogue of the slope of a line is a direction vector −→ v = a −→ ı + b −→ + c −→ k to which it is parallel. 6 Then, to pick out one among all the lines parallel to −→ v , we specify a basepoint P ( x ,y ,z ) through which the line is required to pass. 6 In general, we do not need to restrict ourselves to unit vectors; any nonzero vector will do....
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 Calculus, nonzero vector, geometrically informative version

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