Answer
$m(6ti+2j+6tk)$
or,
$6tmi+2mj+6mtk$
Work Step by Step
Determine the force of a particle with mass $m$ . Apply Newton's Second law of kinematics.
Force vector: $F(t)=ma(t)$
As we are given that $r(t)=t^3i+t^2j+t^3k$
$v(t)=r'(t)=3t^2i+2tj+3t^2k$ and $a(t)=v'(t)=6ti+2j+6tk$
Consider the force vector equation such as $F(t)=ma(t)=m(6ti+2j+6tk)$
$F(t)=m(6ti+2j+6tk)$
or,
$F(t)=6tmi+2mj+6mtk$
