The distance of the plane $2x - y - 2z - 9 = 0$ from the origin is $d$ units.

The acute angle between the planes $2x - y + z = 6$ and $x + y + 2z = 3$ is ......... $^o$.

If a variable plane,at a distance of $3 \ units$ from the origin,intersects the coordinate axes at $A, B$,and $C$,then the locus of the centroid of $\Delta ABC$ is

The equation of the plane passing through the points $(2,1,0)$,$(3,2,-2)$,and $(3,1,7)$ is

Let $\pi_1$ be the plane passing through the points $(0,1,2), (1,0,-2), (-2,1,0)$ and $\pi_2$ be the plane passing through the point $(1,2,3)$ and perpendicular to the planes $x+y+z=1$ and $2x-3y+z=5$. If $\theta$ is the acute angle between the planes $\pi_1$ and $\pi_2$, then $\cos \theta=$

Find the vector and Cartesian equations of the plane that passes through the point $(1, 4, 6)$ and the normal vector to the plane is $\hat{i} - 2\hat{j} + \hat{k}$.