Consider the planes $P_1,P_2$ and points A(2, 5, 1) and B(1, 3, 0) where
 $\begin{array}{r}{P}_1:x+y+z=3\\ P_2:2x+y-z=4\end{array}$
Then which is/are CORRECT ?

Projection of segment AB on P₁ is equal to $2\sqrt{2}\text{ units }$

Area enclosed by locus of all points on P₁ which are at a distance of 3 units from B is equal to $\frac{26\pi }{3}\mathrm{sq}$. units.

Projection of segment AB on P₁ is equal to $\frac{\sqrt{6}}{3}$units

Shortest distance between line AB and points common to ${\mathrm{P}}_1,{\mathrm{P}}_2$ is equal to $\frac{1}{5\sqrt{3}}$units.