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

The Cartesian equation of the plane whose vector equation is $\vec{r}=(1+\lambda-\mu) \hat{i}+(2-\lambda) \hat{j}+(3-2 \lambda+2 \mu) \hat{k}$,where $\lambda, \mu$ are scalars,is:

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 -

$A$ point lying on the plane that passes through the points $\hat{i}-\hat{j}+\hat{k}$,$\hat{i}-2\hat{j}+3\hat{k}$,and $\hat{i}+2\hat{j}-3\hat{k}$ is:

The coordinates of the foot of the perpendicular drawn from the origin to the plane $3x + 2y + 6z = 56$ are:

In $3$-dimensional space,the equation $x^2-8x+12=0$ represents ....