A curve given parametrically by (x,y,z)=(−1+3t, 2−2t^2, −t+2t^3). There is a unique point P on the curve with the property that the tangent line at P passes through the point (8,−8,11). The point P has coordinates... ?
Hmm not quite sure where to start.

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the tangent to the postion vector is just the derivatives of the components..

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