A plane $\pi$ is passing through the points $A(1,-2,3)$ and $B(6,4,5)$. If the plane $\pi$ is perpendicular the plane $3 x-y+z=2$, then the perpendicular distance from $(0,0,0)$ to the plane $\pi$ is

The point of intersection of the lines represented by $\mathbf{r}=(\hat{\mathbf{i}}-6 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})+\mathbf{t}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})$ and $\mathbf{r}=(4 \hat{\mathbf{j}}+\hat{\mathbf{k}})+\mathbf{s}(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}})$ is

If the four points $(6,2,4),(1,3,5),(1,-2,3)$ and $(6, k, 2)$ are coplanar, then $k=$

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