If the plane $7x + 11y + 13z = 3003$ meets the coordinate axes at $A, B, C$,then the centroid of the $\triangle ABC$ is

The distance of the point $(2, -1, 0)$ from the plane $2x + y + 2z + 8 = 0$ is

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

Direction ratios of the normal to a plane passing through $(1, 0, 0)$ and $(0, 1, 0)$ which makes an angle of $\frac{\pi}{4}$ with the plane $x + y - 3 = 0$ are:

Let the image of the point $P(1, 2, 6)$ in the plane passing through the points $A(1, 2, 0)$,$B(1, 4, 1)$,and $C(0, 5, 1)$ be $Q(\alpha, \beta, \gamma)$. Then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to :

If the foot of the perpendicular drawn from the origin to the plane is $(3, 2, 1)$,then the equation of the plane is