$G(1,0,1)$ is the centroid of the $\triangle A B C$. If $A=(1,-4,2)$ and $B=(3,1,0)$, then $A G^2+C G^2=$

If the sum of the distances of the point $(3,4, \alpha), \alpha \in R$ from $X$-axis, $Y$-axis and $Z$-axis is minimum, then $\sec \alpha=$

If the equation of the plane passing through the point $(2,-1,3)$ and perpendicular to each of the planes $3 x-2 y+z=8$ and $x+y+z=6$ is $l x+m y+n z=1$, then $4 m+2 n-3 l=$

$$ \mathop {\lim }\limits_{x \to \infty } \frac{(\sqrt{2})-\sqrt{1+\cos x}}{\sqrt{15+\cos 2 x-4}}= $$