The direction cosines of a normal to the plane passing through $(4,2,3),(-1,4,2)$ and $(3,2,1)$ are …..

The equation of the plane passing through the point $(1,1,1)$ and through the line of intersection of $x+2 y-z+1=0$ and $3 x-y-4 z+3=0$ is

If the foot of the perpendicular drawn from the origin to a plane is $\mathrm{P}(-1,-1,2)$, then equation of the plane is

The angle between lines whose direction cosines satisfy the equation $l+m+n=0$ and $l^2-\mathrm{m}^2-\mathrm{n}^2=0$, is