A particle has the following acceleration expressed in the rectangular coordinate system

by its components $a_x=3[m{s}^{-2}],a_y=2v_y[m{s}^{-2}],a_z=3t[m{s}^{-2}]$

Determine the following kinematical quantities vec$(r),$vec$(),$vec$(a),$vec$(a_{}),$vec$(g_n)$ in the vector form, and

radius $$ of the curvature, at time interval $t=6s.$

$(18$ marks$)$