If the plane $3x - 2y - z - 18 = 0$ meets the coordinate axes at $A, B, C$,then the centroid of $\triangle ABC$ is

Find the vector and cartesian equations of the plane which passes through the point $(5, 2, -4)$ and is perpendicular to the line with direction ratios $2, 3, -1$.

Let $\bar{n}$ be a vector of magnitude $3\sqrt{3}$ such that it makes equal acute angles with the coordinate axes. Then the vector equation of a plane passing through $(1, -1, 2)$ and normal to $\bar{n}$ is:

Find the Cartesian equation of the following plane: $\vec{r} \cdot(\hat{i}+\hat{j}-\hat{k})=2$

If $O$ is the origin and the coordinates of $P$ are $(1, 2, -3)$,then the equation of the plane passing through $P$ and perpendicular to $OP$ is

The equation of a plane containing the point $(1, -1, 2)$ and perpendicular to the planes $2x + 3y - 2z = 5$ and $x + 2y - 3z = 8$ is