I would like to show that (cxb).a = (axc).b in Rn where x denotes the cross product and . denotes the dot product. Since the cross product is only defined in R1, R3, and R7, my inclination is to prove the above equation in cases (case one being a,b,c are vectors in R1, etc). However, this seems a bit tedious, particularly for R7. I am familiar with the Triple Product in R3, but am unsure if it applies in Rn, and if so how to prove it. If so, this seems like a much quicker and more concise proof. Please help! Any assistance is greatly appreciated. Thanks!