For the curve r(t)=(tcost,tsint,e−t)r(t) = (t \cos t, t \sin t, e^{-t})r(t)=(tcost,tsint,e−t), find the unit tangent vector T(0)\mathbf{T}(0)T(0).
12(1,0,−1)\frac{1}{\sqrt{2}}(1, 0, -1)21(1,0,−1)
12(0,1,−1)\frac{1}{\sqrt{2}}(0, 1, -1)21(0,1,−1)
13(1,1,−1)\frac{1}{\sqrt{3}}(1, 1, -1)31(1,1,−1)
(0,0,1)(0, 0, 1)(0,0,1)