The direction cosines of two lines are connected by the relations $l-m+n=0$ and $2 l m-3 m n+n l=0$. If $\theta$ is the angle between these two lines, then $\cos \theta=$

A plane $\pi$ passes through the points $(5,1,2),(3,-4,6)$ and $(7,0,-1)$. If $p$ is the perpendicular distance from the origin to the plane $\pi$ and $l, m$ and $n$ are the direction cosines of a normal to the plane $\pi$, the $|3 l+2 m+5 n|=$

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 $\cos \theta=$