- #1

nomadreid

Gold Member

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^{→}(t) = f(t)*i

^{→}(t)+g(t)*j

^{→}(t)+h(t)*k

^{→}(t) as finding "the" tangent vector r'

^{→}(t) = f'(t)*i

^{→}(t)+g'(t)*j

^{→}(t)+h'(t)*k

^{→}(t) and normalizing it, and further with finding "the" tangent line at t=t

_{0}as r(t

_{0}) + r'(t

_{0})*t . (If I got that right.) But if one thinks of a tangent line as a line being perpendicular to the curve at the given point, then there are an infinite number of tangent lines (and unit tangent vectors), which is, as I understand it, the reason one deals with tangent planes in respect to curves in 3-D instead of tangent lines. What am I missing here?