 In this video, we will present the solution to question number two from practice exam two for math 2270 We are asked to compute the norm of 3u plus 2v minus w So to begin with we need to compute just this linear combination 3u plus 2v minus w It's gonna move this around to get a little bit more space on the screen So if we take if we compute that that vector there 3u plus 2v minus w This is going to equal We're gonna multiply u by 3 so we get 6 0 and negative 3 We're gonna multiply v by 2 so we get negative 2 negative 2 Plus 6 and then we're gonna tie we're just gonna subtract w so we get minus 3 plus 1 and plus 2 So we then compute this value This will give us 6 minus 5 which is 1 We're gonna get 0 minus 2 plus 1 which is a negative 1 and then you're gonna get 6 plus 2 Is 8 minus 3 is 5 So this is the vector. We need to take its length now when you compute the norm of a vector Remember this is equal to the square root of x dot x which this turns out just to make it the square root of a of a bunch of Sum of squares right x 1 squared plus x 2 squared all the way down to x n squared That's the basic formula here now be aware that if you are taking If you're taking complex numbers right here, you're actually gonna get a sum of the complex numbers The squares there so for like example If we took the length of the vector 1 plus 2i and then 3i You know something like that in that situation You're gonna get the square root of 1 squared plus 2 squared plus 3 squared So you're gonna take the sum of all the both the real part imagining parts separately Now in this vector in this problem, we just have a real vector. So we don't have to worry about that the length The length of the vector this is gonna be the square root of we're gonna get 1 squared plus 1 squared plus 5 squared 5 squares 25 You're gonna add uh, you're gonna add 2 to that so we get the square root of 27 in which I don't see that on the list That's because 27 can be factors 9 times 3 where 9 is a perfect square So this becomes 3 root 3 and this would then tell us the correct answer is d So