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AI InttuctionsPARALLEL Vectors: Twc ucctors Arc Danhlalif thcv arc pnin-ing thc cxact carne durectdn tne Olagram belcu, the blue Jreen vecIons are paralle eag oter ...

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AI InttuctionsPARALLEL Vectors: Twc ucctors Arc Danhlalif thcv arc pnin-ing thc cxact carne durectdn tne Olagram belcu, the blue Jreen vecIons are paralle eag oter but neitner onz paralle the crange vectorANTI-PARALLEL VECTORS: Tuo vectons antk-paraller polniing tthc cxact oppositc dircczion, thc diagrom bclow, thc purplc vcctor is anti - pareei nereO YeCio -PERPENDICULAR VEcTORS: Two Yocrors Jm perpandicular if thc anglc belween che Directi ons chey 2re pcinbno the dlagram belou gold vector pem

AI Inttuctions PARALLEL Vectors: Twc ucctors Arc Danhlalif thcv arc pnin-ing thc cxact carne durectdn tne Olagram belcu, the blue Jreen vecIons are paralle eag oter but neitner onz paralle the crange vector ANTI-PARALLEL VECTORS: Tuo vectons antk-paraller polniing tthc cxact oppositc dircczion, thc diagrom bclow, thc purplc vcctor is anti - pareei nereO YeCio - PERPENDICULAR VEcTORS: Two Yocrors Jm perpandicular if thc anglc belween che Directi ons chey 2re pcinbno the dlagram belou gold vector pemendicular the gry vector Use Iheea dellmong denidy parallel ecicre an-parallel ecicre and pemendicular %actorb



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Determine which of the vectors is (are) parallel to $\mathrm{z}$. Use a graphing utility to confirm your results. $\mathbf{z}=\frac{1}{2} \mathbf{i}-\frac{2}{3} \mathbf{j}+\frac{3}{4} \mathbf{k}$ (a) $6 \mathbf{i}-4 \mathbf{j}+9 \mathbf{k}$ (b) $-\mathbf{i}+\frac{4}{3} \mathbf{j}-\frac{3}{2} \mathbf{k}$ (c) $12 \mathbf{i}+9 \mathbf{k}$ (d) $\frac{3}{4} \mathbf{i}-\mathbf{j}+\frac{9}{8} \mathbf{k}$

Okay, So the initial point of Hugh Mars position of the terminal point of PR. So by trying the law of the Somme off peak you plus you are it's equal to the vector with initial point P and terminal point, our says p r. Rights, that's part a four for part B by the trying the law R p So are we plus PS PS is simply the vector rs o r s right? It's the next you have apart. See, So we have qs minus P s. So first we consider us minus P s as que es plus negative gs since native yes is the same length is PS but points in the opposite direction we have naked PS is equal to P s So therefore us minus p s could be viewed ist us plus p s which is just equal to Cuba. This is equal to que pique part c and finally party. We have rs plus SP plus speak You so using the trying law twice. So if we have Rs plus s p s p plus p Q so you've been trying to love twice the first part So R s plus s P is equal to you, r p plus p Q, which is equal to our cute

Christian position vector of A. B, C and D. Are given. No we will do. They will find factor A B. Now. Actually big will position vector of b minus position vector of a means I plus two J plus three k minus do I Plus three J Plus five Kids. That is equal to -1 -J. No we will find C. D. This is the position vector of the minus position. Electoral See means I plus 10. J plus 10-K minus minus five. I Plus four J -2. Okay. Which comes out to the six I plus six. Yeah plus 12. Okay. Equal We will take six common. I We will take -6 common. That will be equal to minus six equals minus I I -J -2. Okay Which is equal to -6. Be vector means C. D. Well minus six times a B vector. So we can say this implies maybe yes peddler too. City. All cities parlor too. Maybe means option. See is correct.

Question here were given the to, uh, question realized So the are won t in court during the three minus 14 plus the times in the eight around 16 And then we have the aren't you d ego to the 11. 11 minus to plus the times the 46 months. Three. Now notice them from the second equation here it would, aren't you? After the, uh, minus, do you? And then we get equal to the 11. 11 months, Two months, two times, 46 months. Three. Then we get equal to the three and then minus one on the farm here and which is exactly equal to the bone in the first, uh, question here and then another thing. We know that the factor Direction 31 equal to the eight trail on the sixth. It can be written down into the you can factor. I wanted them Uganda for six months. Three. So it will be equal to the two times the video will be this one. They're far from here. We can conclude that there are one day will be identical to the arch duty here

For the given problem we know that Z has an initial 0.1 negative 13 and a terminal point negative 235 Um So we want to determine if the vectors are parallel to see will keep in mind that given the terminal and initial point we can figure out our vectors. So This vector out here is gonna be -2 -1 which is -3. And then three minus negative one which is four And then 5 -3 which is to. So this is our new vector and we want you to come in um if these other vectors are parallel or not. So we see that the first factor will be parallel because it's two times um that vector so it's negative six Um negative or positive eight positive for. So we see that this factor is actually parallel to its to the original vector, This is -6. So these vectors are parallel.


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