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Finding the vector tex2html_wrap_inline270

Finding the tangent vector is easy. If we think of t as time, then the vector tex2html_wrap_inline332 gives our position on C as a function of time. Thus, our velocity vector is always tangent to our path. But, we know that

equation36

so that means that at each of the N + 1 points, we have

equation41

This relationship is really just the differential form of the familiar equation ``distance = rate tex2html_wrap_inline340 time''. Note that tex2html_wrap_inline342 is really a displacement vector between the ith and i+1th points on the curve C and tex2html_wrap_inline350 is the time it takes to get from the ith to the i+1th point. In general, we take a uniform step between points so that tex2html_wrap_inline356 .


Vector Calculus
Sun Jul 27 11:36:39 MST 1997