$A$ point on the plane determined by the points $A(1,1,-1)$, $B(2,-1,0)$, and $C(-1,0,2)$ among the following is:

The length of the perpendicular from the origin to the plane which makes intercepts $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively on the coordinate axes is

Find the equation of a plane that is at a unit distance from the origin and is parallel to the plane $x - 2y + 2z - 5 = 0$.

If the foot of the perpendicular from $(0,0,0)$ to the plane is $(1,2,2)$,then the equation of the plane is

$\vec{n}$ is a unit vector normal to the plane $\pi$ containing the vectors $\hat{i}+3 \hat{k}$ and $2 \hat{i}+\hat{j}-\hat{k}$. If this plane $\pi$ passes through the point $(-3,7,1)$ and $p$ is the perpendicular distance from the origin to this plane $\pi$, then $\sqrt{p^2+5}=$

$A$ plane is at a unit distance from the origin. It cuts the coordinate axes at $P, Q,$ and $R$ respectively. If the locus of the centroid of the $\Delta PQR$ is $\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = k$,then $k =$