EXAMPLE $1\mathrm{.}6$

Relative to a Cartesian coordinate system, the position, velocity, and acceleration of a particle $P$ at a given instant are

$r=250$hat$(i)+630$hat$(j)+430$hat$(k)(m)$

$v=220$hat$(i)+222$hat$(j)+32$hat$(k)(\frac{m}{s})$

$a=16i+125$hat$(j)+30$hat$(k)(\frac{m}{s^2})$

Find the coordinates of the center of curvature at that instant.