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? 
 A: To ease the problem, assume that one of the planes ($P$) is $z=0$ and the hinge is $r:y=z=0$.
The equation of the plane that cuts $P$ at $r$ with an angle $\alpha$ is $Q:y\sin\alpha+z\cos\alpha=0$. We can assume that $0<\alpha\le\pi/2$.
Now, a generic vector in $P$ is $(u,v,0)$ and a generic vector of the same length in $Q$ is $(u,v\cos \alpha, v\sin\alpha)$, so the cosine of the acute angle $\beta$ between them is
$$\cos\beta=\frac{u^2+v^2\cos \alpha}{u^2+v^2}\ge\frac{u^2\cos\alpha+v^2\cos \alpha}{u^2+v^2}=\cos\alpha$$
So $\beta\le \alpha$.
That is, the acute angle between two vectors is at most the acute angle between two planes that contain them.
A: 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.
A: The (acute) angle between pairs of vectors can be anything from $0$ to $180°$. Consider a pair of vectors that are both in the hinge—pointing in the same direction along the line of intersection of the two planes. Clearly, the angle between them is zero. Now, rotate one of these vectors in its plane. The angle between them will change continuously until it reaches a maximum of $180°$ when the vector is back in the hinge, but pointing in the opposite direction.
