Transcription of Vector Functions - Whitman College
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Vector Functions - Whitman College
13 Vector eCurvesWe have already seen that a convenient way to describe a line in three dimensions is toprovide a Vector that points to every point on the line as a parametertvaries, likeh1,2,3i+th1, 2,2i=h1 +t,2 2t,3 + that this gives a particularly simple geometric object, there is nothing special aboutthe individual Functions oftthat make up the coordinates of this Vector any Vector witha parameter, likehf(t), g(t), h(t)i, will describe some curve in three dimensions astvariesthrough all possible the curveshcost,sint,0i,hcost,sint, ti, andhcost,sint, , the first two coordinates in all three Functions trace out the points on theunit circle, starting with (1,0) whent= 0 and proceeding counter-clockwise around thecircle astincreases.
Except that this gives a particularly simple geometric object, there is nothing special about the individual functions of t that make up the coordinates of this vector—any vector with a parameter, like hf(t),g(t),h(t)i, will describe some curve in three dimensions as t …
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