For each of the following statements, determine whether it is true or false. If the statement is true then prove it; if it is false then give an example where the statement fails to hold.

(i) If

u, v,w is a right-handed triple of vectors, with u orthogonal to v, then v must be orthogonal to w.

(ii) (u × v) × w = u × (v × w) for all vectors u, v,w.

(iii) If u × v = v × u then we must have u × v = 0.

(iv) If u is a vector such that u × v = 0 for every vector v, then we must have u = 0.

can some one help me asap i dnt knw wer 2 start .