Prove: For any vectors u, v, and w in a vector space V:

the vectors u-v, v-w, w-u and form a linearly dependent set.

The answer is obvious; because
(u-v)+(v-w)+(w-u) = 0 [identity true for any u, v and w].
So any one of them,say (u-v) can be written as:
(u-v)= (-1)*(v-w)+(-1)*(w-u) and so on!