Suppose I know the following 3 normalized vectors in 3-D Euclidean space:
$\frac{\vec{A}}{||\vec{A}||}$,
$\frac{ \vec{A} + \vec{B}}{||\vec{A} + \vec{B}||}$
$\frac{ \vec{A} + \vec{C}}{||\vec{A} + \vec{C}||}$
Is it possible to determine the 3 unknown vectors $\vec{A}, \vec{B}, \vec{C}$ ?