Let $\Pi$ be a plane containing the points $(0,-5,-1),(1,-2,5),(-3,5,0)$ and $L$ be a line passing through the point $(0,-5,-1)$ and parallel to the vector $\hat{\mathbf{i}}+5 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}$. Then the length of the projection of the unit normal vector to the plane $\Pi$ on the line $L$ is

If the line passing through the points $(a, 2,-4)$ and $(5,3, b)$ crosses the $Z X$-plane at the point $(-a+2 b, 0, a+b)$, then $14 a+7 b$

The direction cosines of the normal to the plane containing the lines having direction ratios $1,2,1$ and 4,5, -3 are

The foot of the perpendicular drawn from the point $(1,1,1)$ to the plane $\pi_1$ is $(1,3,5)$. If $(2,2,-1),(3,4,2)$, $(3,3,0)$ are three points on the plane $\pi_2$, then the angle between the planes $\pi_1$ and $\pi_2$ is