If the circumcenter of the triangle formed by the points $(1,2,3),(3,-1,5)$ and $(4,0,-3)$ is $(\alpha, \beta, \gamma)$, then $|\alpha|+|\beta|=$

If $\theta$ is the acute angle between the two lines whose direction cosines are connected by the relations $l+m+n=0$ and $2 l m+2 n l-m n=0$, then $\cos \theta=$

If the foot of the perpendicular drawn from the point $(1,0,-2)$ to the plane $\pi$ is $(2,0,-1)$ and the equation of the plane $\pi$ is $a x+b y+c z=2$, then $a^2+b^2+c^2=$

If $A(1,2,3), B(3,7,-2), C(6,7,7)$ and $D(-1,0,-1)$ are points in a plane, then the vector equation of the line passing through the centroids of $\triangle A B D$ and $\triangle A C D$ is