Let $A$ is set of all possible planes passing through four vertices of given cube. Find number of ways of selecting four planes from set $A$, which are linearly dependent and one common point. (If planes $P_1 = 0$, $P_{2}=0, P_{3}=0$ and $P_{4}=0$ can be writen as $a P_{1}+b P_{2}+c P_{3}+d P_{4}=0$, where all $a, b, c, d$ are not equal to zero, then we say planes $P_{1}, P_{2}, P_{3}, P_{4}$ are linearly dependent planes).
Let OABC is a regular tetrahedron and $P$ is any point in space. If edge length of tetrahedron is 1 unit. find the least value of $2\left(\mathrm{PA}^{2}+\mathrm{PB}^{2}…