$A(1,2,3), B(2,3,1)$ and $C(3,1,2)$ are three points. If the point $P$ divides $A B$ in the ratio $1: 2$ and the point $Q$ divides $B C$ in the ratio $-2: 3$, then the distance between $P$ and $Q$ is

If the image of the point $(1,-2,1)$ with respect to the line passing through the points $B(1,1,2)$ and $C(2,2,1)$ is $(l, m, n)$, then $l^2+m^2+n^2=$

A plane $\pi$ passing through the point $(1,1,1)$ is perpendicular to the line joining the points $(6,3,2)$ and $(1,-4,-9)$. If $a x+b y+c z-23=0$ is the equation of the plane $\pi$, then $a+b-c=$

The point of intersection of the line passing through the point $\hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and the plane passing through the points $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}, 2 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{k}}$ is