Find the distance of a point $(2, 5, -3)$ from the plane $\vec{r} \cdot (6 \hat{i} - 3 \hat{j} + 2 \hat{k}) = 4$. (in $/7$)

The coordinates of the foot of the perpendicular drawn from the origin to the plane $3x + 2y + 6z = 56$ are:

$A$ variable plane is at a constant distance $p$ from the origin and meets the axes in $A, B$ and $C$. The locus of the centroid of the tetrahedron $OABC$ is

If $M$ is the foot of the perpendicular drawn from $P(1, 2, -1)$ to the plane passing through the point $A(3, -2, 1)$ and perpendicular to the vector $\vec{n} = 4\hat{i} + 7\hat{j} - 4\hat{k}$,then the length of $PM$,in proper units,is

The equation of the plane passing through $(1, 1, 1)$ and $(1, -1, -1)$ and perpendicular to $2x - y + z + 5 = 0$ is:

$A$ plane passing through the points $(0, -1, 0)$ and $(0, 0, 1)$ and making an angle $\frac{\pi}{4}$ with the plane $y - z + 5 = 0$ also passes through the point