linear algebra – Prove that three vectors are coplanar

Three vectors are given: u, v, w. It is given that:
| u | = | v | = | w | = sqrt (2); u ∙ v = u ∙ w = v ∙ w = -1.
Prove that the vectors u, v, w are coplanar (in the same plain).

I have some ideas, but I do not know if they are useful in this case:

I know that three vectors are coplanar if u ∙ (v x w) = 0.
Plus, I guess you can prove it with a linear dependence, but I do not know how to use it here.

Moreover, I thought that the angle between the vectors could be useful – 120 degrees between 2 vectors – but does that necessarily mean that they are on the same coplanar plane?