Distance between the two planes: $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is

The direction ratios of the two lines $AB$ and $AC$ are $1, -1, -1$ and $2, -1, 1$. The direction ratios of the normal to the plane $ABC$ are

If the angle between the planes $ax - y + 3z = 2a$ and $3x + ay + z = 3a$ is $\frac{\pi}{3}$,then the direction ratios of the line perpendicular to the plane $(a+2)x + (a-4)y + 2az = a$ are

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

$A$ tetrahedron has vertices $O(0,0,0)$,$A(1,2,1)$,$B(2,1,3)$,and $C(-1,1,2)$. If $\theta$ is the angle between the faces $OAB$ and $ABC$,then $\cos \theta =$

$A$ plane passing through the points $A(2, 3, 5)$ and $B(-3, -5, -7)$ is perpendicular to the plane $x - y + z = 1$. Which of the following points lies on this plane?