Prove points are coplanar 
I have that $AX = BX, AW=BW, AY = BY, AZ=BZ$
No matter how, I can't imagine that this points necessarily need to be coplanar, but the exercise asks me to do it: prove that $W,X,Y,Z$ are coplanar.
Any help?

A plane of points $p$ is can be defined by the equation 
$$p \circ N = 1$$
for some vector $N$, where $\circ$ is the dot product (except for a plane through the origin which is $p \circ N = 0$).  
Consider the expression "all points that are equidistant from $A$ and $B$".  Does this expression characterize a plane?
$$\sqrt{(X - A)\circ (X - A)} = \sqrt{(X - B)\circ (X - B)}$$
$$(X - A)\circ (X - A) = (X - B)\circ (X - B)$$
$$X \circ X - 2\cdot X \circ A + A \circ A = X \circ X - 2 \cdot X \circ B + B \circ B$$
$$2 \cdot X \circ A - 2 \cdot X \circ B = A \circ A - B \circ B$$
$$X \circ \left(\frac{2~(A - B)}{A \circ A - B \circ B}\right) = 1$$
So yes, it is a plane equation.
