The coordinates of the point where the line joining $(1, 1, 1)$ and $(2, 2, 2)$ intersects the plane $x + y + z = 9$ are:

If $P=(0,1,0)$ and $Q=(0,0,1)$,then the length of the projection of the line segment $PQ$ on the plane $x+y+z=3$ is:

$A$ symmetrical form of the line of intersection of the planes $x = ay + b$ and $z = cy + d$ is

Let the planes be $3x - 6y - 2z = 15$ and $2x + y - 2z = 5$.
Statement-$1$: The parametric equations of the line of intersection of the given planes are $x = 3 + 14t, y = 1 + 2t, z = 15t$.
Statement-$2$: The vector $14\hat{i} + 2\hat{j} + 15\hat{k}$ is parallel to the line of intersection of the given planes.

If the plane $3x - 4y - kz = 7$ contains the line $\frac{1 - x}{-2} = \frac{y + 1}{3} = \frac{z}{4}$,find the value of $k$.

If the plane $2x + y - 5z = 0$ is rotated about its line of intersection with the plane $3x - y + 4z - 7 = 0$ by an angle of $\frac{\pi}{2}$,then the plane after the rotation passes through the point