 In this video we will provide the solution to question number seven from practice exam three for math 2270 for which we're given a vector u which we know it has a length of five and we're asked to compute the cross product of 2u and 3u for which you might wonder what does the length of the vector do for us how does that help us out this calculation well when it comes to the cross product the cross product is a bilinear map so scalars in the first and second factor can be factored out so if you factor out the first scalar you're gonna get two times u cross 3u and then if we factor out the three you're gonna end up with two times three times u cross u and yes two times three is six but one thing to remember about the cross product here is that the cross product of a vector with itself is always equal to zero and so we end up with six times the zero vector for which anything times the zero vector is going to be zero and this tells us then that the correct answer would then be a the zero vector and so the length of the vector being five is just a red herring it's superfluous information that doesn't actually help us with the calculation here