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

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

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

The direction ratios of the normal to the plane passing through the points $(1, 0, 0)$ and $(0, 1, 0)$ and making an angle of $\pi/4$ with the plane $x + y = 3$ are proportional to:

From a point $P(a, b, c)$, perpendiculars $PA$ and $PB$ are drawn to $XY$ plane and $ZX$ plane respectively. If $O$ is the origin, then the equation of plane $OAB$ is

If $L_1$ and $L_2$ are two lines which pass through the origin and have direction ratios $(3, 1, -5)$ and $(2, 3, -1)$ respectively,then the equation of the plane containing $L_1$ and $L_2$ is