The equation of the plane which is parallel to the $xy$-plane and cuts an intercept of length $3$ from the $z$-axis is

The equation of a plane parallel to the $x$-axis is:

$A$ tetrahedron has vertices at $P(2,1,3)$,$Q(-1,1,2)$,$R(1,2,1)$ and $O(0,0,0)$. The angle between the faces $OPQ$ and $PQR$ is

The direction ratios of the normal to the plane passing through the points $(1, 0, 0)$ and $(0, 1, 0)$ and making an angle of $\pi/4$ with the plane $x + y = 3$ are proportional to:

Find the distance from the origin to the plane passing through the point $(2, 3, -1)$ and perpendicular to the vector $3\hat{i} - 4\hat{j} + 7\hat{k}$.

The image of the point $(1, 2, -1)$ on the plane containing the line $\frac{x + 1}{-3} = \frac{y - 3}{2} = \frac{z + 2}{1}$ and the point $(0, 7, -7)$ is: