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

The circumcenter of the triangle formed by lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ 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

If $\quad \overline{\mathrm{a}}=\lambda x \hat{\mathrm{i}}+y \hat{\mathrm{j}}+4 z \hat{\mathrm{k}}, \quad \overline{\mathrm{b}}=y \hat{\mathrm{i}}+x \hat{\mathrm{j}}+3 y \hat{\mathrm{k}}$, $\overline{\mathrm{c}}=-z \hat{\mathrm{i}}-2 z \hat{\mathrm{j}}-(\lambda+1) \hat{\mathrm{k}} x$ are the sides of the triangle ABC , where $x, y, \mathrm{z}$ are not all zero, such that $\bar{a}+\bar{b}-\bar{c}=\overline{0}$, then value of $\lambda$ is