The points $A(-1,2,3), B(2,-3,1)$ and $C(3,1,-2)$

The directions cosines of the line making angles $\frac{\pi}{4}, \frac{\pi}{3}$ and $\theta\left(0<\theta<\frac{\pi}{2}\right)$ respectively with $X, Y$ and $Z$ axes are

If the equation of the plane passing through the point $(3,2,5)$ and perpendicular to the planes $2 x-3 y+5 z=7$ and $5 x+2 y-3 z=11$ is $x+b y+c z+d=0$, then $2 b+3 c+d=$

The circumradius of the triangle formed by the points $(2,-1,1),(1,-3,-5)$ and $(3,-4,-4)$ is