Find the equation of the plane passing through the point $(1, 2, -3)$ and parallel to the plane $3x - 5y + 2z = 11$.

Find the distance of the point $(0, 0, 0)$ from the plane $3x - 4y + 12z = 3$. (in $/13$)

The equation of a plane containing the point $(1, -1, 1)$ and parallel to the plane $2x + 3y - 4z = 17$ is

If $A$ and $B$ are the feet of the perpendiculars drawn from point $Q(a, b, c)$ to the planes $yz$ and $zx$ respectively,then the equation of the plane passing through the points $A, B$ and the origin $O(0, 0, 0)$ is $.........$

If the plane $2x + 3y + 5z = 1$ intersects the coordinate axes at the points $A, B, C$,then the centroid of $\triangle ABC$ is

The angle between the planes $\vec{r} \cdot(2 \hat{i}+4 \hat{j}-3 \hat{k})=5$ and $\vec{r} \cdot(5 \hat{i}+3 \hat{j}+4 \hat{k})=7$ is