If the distance of the point $(1, 1, 1)$ from the origin is half its distance from the plane $x + y + z + k = 0$,then $k = $

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

The equation of the plane bisecting the line segment joining the points $(2,0,6)$ and $(-6,2,4)$ and perpendicular to it,is

The equation of the plane passing through $(1,0,0)$ and $(0,1,0)$ and making an angle of $45^{\circ}$ with the plane $x+y-3=0$ is:

If the plane $\vec{r} = (\lambda + \mu)\hat{i} + (2 + \mu)\hat{j} + (3\lambda + 2\mu)\hat{k}$, where $\lambda$ and $\mu$ are parameters, intersects coordinate axes at points $(a, 0, 0), (0, b, 0), (0, 0, c)$, then $a + b + c = $

The equation of the plane passing through the points $(2,1,0)$,$(3,2,-2)$,and $(3,1,7)$ is