Find the point on the curve ,

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Find the point on the curve r(t)=⟨2cos⁡t,2sin⁡t,et⟩\mathbf{r}(t) = \langle 2 \cos t, 2 \sin t, e^t \rangle, 0≤t≤π0 \le t \le \pi, where the tangent line is parallel to the plane 3x+y=1\sqrt{3}x + y = 1.

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