Unformatted text preview: determine a line: the slope re±ects the direction (or tilt) of the line, and then the y-intercept distinguishes between the various parallel lines with a given slope by specifying a point which must lie on the line. A direction in 3-space cannot be determined by a single number, but it is naturally speci²ed by a nonzero vector, so the three-dimensional 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....
View Full Document
- Fall '08
- Calculus, nonzero vector, geometrically informative version