Angle between pair of vectors from two planes at an angle mutually. Suppose I have 2 planes mutually at an angle to each other. Then two vectors, one from each, would make same angle between them. Is that so? 

If I've understood your question,
call the two planes you described plane A and plane B.
Then consider a vector in plane A, but that is also completely contained in the 'hinge line'.
Also consider a vector in plane B, but that is also completely contained in the 'hinge line'. 
Clearly these two vectors do not have an angle between them of 30 degrees.
