If the plane $x - 3y + 5z = d$ passes through the point $(1, 2, 4)$,then the lengths of intercepts cut by it on the axes of $x, y, z$ are respectively

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

The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2x-y-2z=5$ and $3x-6y+2z=7$ is

Find the equation of the set of points which are equidistant from the points $A(3, 4, -5)$ and $B(-2, 1, 4)$.

Find the equation of the plane passing through the point $(2, 3, 1)$ and perpendicular to the line $\frac{x - 1}{1} = \frac{y - 2}{-1} = \frac{z + 1}{2}$.

If the cartesian equation of the plane passing through the point $\hat{i}+2 \hat{j}+\hat{k}$ and parallel to the vectors $2 \hat{i}+3 \hat{j}+\hat{k}$ and $-\hat{i}+2 \hat{j}-3 \hat{k}$ is $a x+b y+c z=1$,then $18(a+b+c)$ is equal to