The sum of intercepts of the plane $4x + 3y + 2z = 2$ on the coordinate axes is

The distance of the plane $\vec{r} = (\hat{i} - \hat{j}) + \lambda(\hat{i} + \hat{j} + \hat{k}) + \mu(\hat{i} - 2\hat{j} + 3\hat{k})$ from the origin is

$A$ variable plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$,which is at a unit distance from the origin,cuts the coordinate axes at $A, B$,and $C$. If the centroid $(x, y, z)$ of $\triangle ABC$ satisfies $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=k$,then $k$ equals:

If the foot of the perpendicular drawn from the point $(1,0,-2)$ to the plane $\pi$ is $(2,0,-1)$ and the equation of the plane $\pi$ is $ax+by+cz=2$,then $a^2+b^2+c^2=$

Find the equation of the plane with intercepts $2, 3$ and $4$ on the $x, y$ and $z$-axis respectively.

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of $\triangle ABC$ is at the point $(1, 2, 3)$,then the equation of the plane is