Answer
$m(6ti+2j+6tk)$
or,
$6tmi+2mj+6mtk$
Work Step by Step
Given: $r(t)=t^3i+t^2j+t^3k$
In order to calculate the force of a particle, whose mass is $m$ we will take the help of Newton's Second law of motion:
Force vector: $F(t)=ma(t)$
Now,
$v(t)=r'(t)=3t^2i+2tj+3t^2k$ and $a(t)=v'(t)=6ti+2j+6tk$
Thus, Force vector: $F(t)=ma(t)=m(6ti+2j+6tk)$
Hence, the required answer is :
$m(6ti+2j+6tk)$
or,
$6tmi+2mj+6mtk$
