Please help with question J8 and the J STAR question.

J.8 Given u = W E , Compute the | V| = volume of the parallelop- iped determined by u, v, w. J.* (Extra credit.) Suppose u, v, w E R' are linearly independent. Find a geometric criterion in terms of u, v, w for when (uxV) Xw = ux (vXw). (# ) Hint: Assume that (*) is true. Let c = (u x v) x w (and hence, c = u x (v x w)). Then try to see what consequences this has for u, v, w. Then show you can turn this around, i.e., that the criteria you found actually implies (*). It is hopeless to try this in a purely "computational" way; you must think geometrically about the cross products. Actually, if you are clever, there is a simple computation that works for the general case