If the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$ makes an angle $\alpha$ with the positive $X$-axis, then $\cos \alpha=$

$\hat{\mathbf{i}}-2 \hat{\mathbf{j}}$ is a point on the line parallel to the vector $2 \hat{\mathbf{i}}+\hat{\mathbf{k}}$. If $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ is a point on the plane parallel to the vectors $2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{k}}$, then the point of intersection of the line and the plane is

Angle between a diagonal of a cube and a diagonal of its face which are coterminus is

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