[tex]\vec F_3=\langle x,y,z\rangle[/tex] is a force vector such that
[tex]\vec F_1+\vec F_2+\vec F_3=\vec0[/tex]
[tex]\implies\langle10,6,4\rangle+\langle0,3,9\rangle+\langle x,y,z\rangle=\langle0,0,0\rangle[/tex]
[tex]\implies\begin{cases}10+x=0\\9+y=0\\13+z=0\end{cases}\implies x=-10,y=-9,z=-13[/tex]
So the missing force is
[tex]\boxed{\vec F_3=\langle-10,-9,-13\rangle}[/tex]
