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

If the plane $\frac{x}{2} - \frac{y}{3} - \frac{z}{5} = 1$ cuts the coordinate axes at points $A, B,$ and $C$ respectively,then the area of the triangle $ABC$ is:

In the following cases,determine whether the given planes are parallel or perpendicular,and in case they are neither,find the angle between them:
$4x + 8y + z - 8 = 0$ and $y + z - 4 = 0$

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

If a plane meets the axes $X, Y, Z$ in $A, B, C$ respectively such that the centroid of $\triangle ABC$ is $(1, 2, 3)$,then the equation of the plane is

Let $S$ be the set of all real values of $\lambda$ such that a plane passing through the points $(-\lambda^2, 1, 1)$,$(1, -\lambda^2, 1)$,and $(1, 1, -\lambda^2)$ also passes through the point $(-1, -1, 1)$. Then $S$ is equal to