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

A triangle ABC is formed by $\mathrm{A}(1,-1,0)$, $B(3,5,3), C(-11,-5,6)$. The equation of internal angle bisector of angle $A$ is