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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Equation of path

**Physics Forums | Science Articles, Homework Help, Discussion**