$A$ point on the plane passing through the points $(\sqrt{2}, 1, 4)$,$(0, -1, 0)$ and $(0, 0, 1)$ is

$A$ plane meets the coordinate axes at $A, B, C$ respectively such that the centroid of the $\triangle ABC$ is $(2, 3, 5)$. Then, the equation of that plane is

Find the angle between the two planes $3x - 6y + 2z = 7$ and $2x + 2y - 2z = 5$.

The direction cosines of the normal to the plane $x + 2y - 3z + 4 = 0$ are

In the following cases,determine whether the given planes are parallel or perpendicular,and in case they are neither,find the angles between them: $2x - 2y + 4z + 5 = 0$ and $3x - 3y + 6z - 1 = 0$.

Direction ratios of the normal to a plane passing through $(1, 0, 0)$ and $(0, 1, 0)$ which makes an angle of $\frac{\pi}{4}$ with the plane $x + y - 3 = 0$ are: