Vt - 3 find: Vi+3# f(z)f'(r) = E2j{12)+32Previewf'(5) = [112x5 (121+372PreviewShow Answer (+3) Show Answer 0.04893568818739 Questpn 17: (parts: cuiof (par...

Find $u+v, v-u,$ and $2 u-3 v$. $$\mathbf{u}=\left\langle\frac{2}{3}, 4\right\rangle, \mathbf{v}=\left\langle-7, \frac{19}{3}\right\rangle$$

Hello, everybody. In this video, I'm gonna be showing you how to solve Exercise six in chapter 13 Section four of calculus Early. Transcendental. No, this problem tells us that we have two vectors U and V, where you has a magnitude of three and v a magnitude of four. And the angle that separates them is two pi over three. And this question wants us to find the magnitude of the cross product You cross V to do this. Recall the ERM 13 0.3 and this gives us a formula. But the magnitude cross product of two vectors is equal to the product of their magnitudes times the sign of their angle of separation. So all we have to do is plug in the values that they give us in this problem. For the magnitude of you, we have three for the magnitude of V. We have four. And then for data, we have the sign of two pi over three. Solving this out even more three times four gives us 12 and then recall that the sign of two pi over three is the same as a sign of pi over three, which is the square root of three divided by two. Then our last step here is to simplify the Fraction 12 and two to make six. And this gives us our answer six times the square root of three. And that's how you solve exercise six.

So in this question may have been provided the balance off you and we and we need to find U plus three v minus you. And to you, my Mr every. So you Plus free will be quarto three coma, three room two plus for you to 11 This will be quarto three plus for two Homa three or two plus one. Similarly remain issue will be quarto Ford Octo Coma one minus three. Coma 32 This should be quarto four minus three. Home. A one minus treated toe. This is a lovely minus you. Similarly to U minus three V will be quarto two and 2332 My next three in two for two 111 They shall be called multiple into witches Will get six comma six or two, uh, minus. We're playing three. Witches will get 12 or two. I want to. This will be quartile. Six minutes, toe on six. Route to minus. Terry. Just that I love to U minus trivia

We are given Vector U and V for U minus three Fee yes, four times you eight minus 20 16 24 Negative 12 minus three times be There's 15 negative six three Negative 21 and negative 12. Do the subtraction between corresponding entries, so eight minus 15 That's negative. Seven. Negative 20 minus six Active. 14 16 minus 3 13 24 minus negative. 21 45 Negative 12 minus negative. 12. That's zero. Part B is similar. Five U plus two v So five times factor you that's 10 negative. 25 20 30 15 plus two times factor V 10 Negative four to negative 14 An active eight so equal to 20 minus 29 22 16 a minus 23 part C We need to multiply corresponding entries to find you that be two times five plus negative five times negative too, plus four times one plus six times negative seven plus negative three times negative four. So 10 plus 10 plus four minus 42 plus 12 Negative. Six. The norm off you is square root off you that you square root of two square plus negative five square plus four square Yeah, plus six square plus Negatives. Three square square root off 90 The norm off We It's also square root off V dot Be the square root off five square plus negative to square plus one square plus minus seven square and plus negative four square square with her 95. The projection off factor you onto V is defined to be you dot be divided by the norm off the square times Vector V We have found you that we does negative six over. Normal fee is square root of 95 square times of actor V Does negative 6/95 times a vector V The distance between U and V is defined to be the norm off U minus. V This is square root off tu minus five square plus negative five plus two square plus four minus one square plus six plus seven square and negative three plus four square square root off nine plus nine plus nine plus 169 plus one that's square root off. 197

All right, look. So in this question, we have been given the well of you is a cultural cover off to J and V is equal to recover off three I. So you place we will be pronto taro toe j plus three or five. Similarly remain issue will be for two. I wrote three or five minus two j only to humans Tree we will week or two to and too e route to J minus three in two. The Route three I. This will be full too. Toe my next little tree, right?