(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

r(t) = costi+ 2 sintj

Find the tangent vectorr'(t) and the corresponding unit tangent vectoru(t) at point P:(.5, 3^{.5},0)

2. Relevant equations

r'(t) =r(t)dt

u(t) =r'(t) / |r'(t)|

3. The attempt at a solution

r'(t) = -sinti+ 2costj

|r'(t)| = [sin^{2}t+ 4cos^{2}t]^{.5}

= [1-3cos^{2}t]^{.5}

u(t) = {-sinti+ 2costj} / {[1-3cos^{2}t]^{.5}}

I think I am right so far, however I don't know what I am supposed to due with Point P to find the unit tangent vector at that point.

Thanks in advance for the help.

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# Homework Help: Unit Tangent Vector at a Point

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