The Cartesian equation of the plane $r = (1 + \lambda - \mu )i + (2 - \lambda )j + (3 - 2\lambda + 2\mu )k$ is

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

Let the plane $\pi$ pass through the point $(1,0,1)$ and be perpendicular to the planes $2x+3y-z=2$ and $x-y+2z=1$. Let the equation of the plane passing through the point $(11,7,5)$ and parallel to the plane $\pi$ be $ax+by-z-d=0$. Then,$\frac{a}{b}+\frac{b}{d}=$

$A$ plane $\pi$ makes intercepts $3$ and $4$ respectively on $Z$-axis and $X$-axis. If $\pi$ is parallel to $Y$-axis, then its equation is:

If $S$ is the set of all real values of $a$ such that a plane passing through the points $(-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2)$ also passes through the point $(-1, -1, 1)$,then $S=$

In three-dimensional space,if $f(x, y, z) = xy + xz$,then the locus of all points which satisfy the equation $f(x, y, z) = 0$ is -