Probably too late to help, but ...
Without any recent related training, I see the problem one you can visualize in 3D.
Vectors V(1) and V(2) may define a plane, and any linear combination of the two, like W(1) is in that plane, so W(1), V(1) and V(2) are coplanar.
By the same reasoning
W(2) is coplanar with V(2) and V(3), and
W(3) is coplanar with V(1) and V(3).
The problem is, there is not enough information.
if V(3) is in the same plane as V(1) and V(2), all the vectors involved are coplanar;
if V(3) is not the same plane as V(1) and V(2), then W(1), W(2), and W(3) are not coplanar.
