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

A fighter plane, which can only shoot bullets straight ahead, travels along the path r(t) = <5 - t, 21 - t^2, 3 - (t^3/27)>. Show that there is precisely one time t at which the pilot can hit a target located at the origin.

2. Relevant equations

I think I am supposed to use a form of the equation for vector parametrization for a tangent line at r(t) = L(t) = r(t) + t[r'(t)].

3. The attempt at a solution

I computed the derivative of r(t): r'(t) = <-1, -2t, -(1/9)t^2>. My book shows examples, but they all have a t value to compute the equation at. I don't quite understand how to find a line that goes through the origin that is tangent to where the fighter is straight ahead, since I don't know that spot either. I graphed it on a 3D parameter graph so I could visualize what is going on, but how do I find these settings?

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# Could I get some help on this vector value function?

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