The equation of a path is of the form: [itex]\vec r = \vec r_0 + \vec A t[/itex](adsbygoogle = window.adsbygoogle || []).push({});

If 't' represents time, show that the time of closest approach is:

[tex]t = -\frac{\vec r_0 \cdot \vec A}{|\vec A|^2}[/tex]

I am not really sure on how to proceed about this, but I made a crude approach by assuming [itex]\vec r[/itex] and [itex]\vec r_0[/itex] to be perpendicular. I took the dot product with r_{0}on both sides of given equation.

[tex]-\vec r_0^2 = \vec A \cdot \vec r_0 t[/tex]

I don't think this a right way to solve, please give some suggestions.

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# Homework Help: Equation of path

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