If the sum of the squares of the distance of the point $\mathrm{P}(x, y, \mathrm{z})$ from the co-ordinate axes is 242 , then the distance of the point P from the origin is units.

If the points $\mathrm{A}(2-x, 2,2), \mathrm{B}(2,2-y, 2)$, $\mathrm{C}(2,2,2-\mathrm{z})$ and $\mathrm{D}(1,1,1)$ are coplanar, then the locus of point $\mathrm{P}(x, y, \mathrm{z})$ is

If the lines $\frac{3-x}{2}=\frac{5 y-2}{3 \lambda+1}=5-\mathrm{z}$ and $\frac{x+2}{-1}=\frac{1-3 y}{7}=\frac{4-z}{2 \mu}$ are at right angles, then $7 \lambda-10 \mu=$

If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2 x-y+\sqrt{\lambda} z+4=0$ is such that $\sin \theta=\frac{1}{3}$, then $\lambda+1=$