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? 

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.
