The equations $|x| = p, |y| = p, |z| = p$ in $xyz$ space represent:

Let $P(\lambda, 2, 1)$ be a point on the plane which passes through the point $Q(4, -2, 2)$. If the plane is perpendicular to the line joining the points $A(-2, -21, 29)$ and $B(-1, -16, 33)$,then find the value of $\left(\frac{\lambda}{11}\right)^{2} - \frac{4\lambda}{11} - 4$.

The plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1$ cuts the axes at points $A, B,$ and $C$. Find the area of $\Delta ABC$.

Find the equation of the plane passing through the point $(\alpha, \beta, \gamma)$ and parallel to the plane $x + y + z = 0$.

If $(2, -1, 3)$ is the foot of the perpendicular drawn from the origin $(0, 0, 0)$ to a plane,then the equation of that plane is:

The distance of the point $(2, -1, 0)$ from the plane $2x + y + 2z + 8 = 0$ is