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Given the displacement vector D (2i 7j) m_ find the displacement vector (in m) R so that D + R = 6Dj (Express your answer in vector form:)7 _ 6v53 )j + 2i...

Question

Given the displacement vector D (2i 7j) m_ find the displacement vector (in m) R so that D + R = 6Dj (Express your answer in vector form:)7 _ 6v53 )j + 2i

Given the displacement vector D (2i 7j) m_ find the displacement vector (in m) R so that D + R = 6Dj (Express your answer in vector form:) 7 _ 6v53 )j + 2i



Answers

Given the displacement vector $\overrightarrow{\mathbf{D}}=(3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}) \mathrm{m}$ find the displacement vector $\overrightarrow{\mathbf{R}} \quad$ so that $\overrightarrow{\mathbf{D}}+\overrightarrow{\mathbf{R}}=-4 D \hat{\mathbf{j}}$

Yeah. Alright. So first we want to calculate this vector C, which is just the some the two vectors on that is going to give us five. I had, uh, minus J hat. Um, minus three K hat. Yeah. Next, we want to calculate the magnitudes. The magnitude of C is gonna be pretty easy. Just gonna be five squared plus one squared minus, uh, plus minus three squared square root. That's basically going is 25 plus nine jizz 34 plus one, which is just gonna be the square root 35. Next. We want to calculate this vector D which is going to be to a minus the green doing that. We're going to get for I hat minus 11 J hat plus 15. Que hat. I apologize. Minus 15 K hat mixed up. One sign there. Um, next, we want to calculate the magnitude, which is just going to be four squared plus 11 squared, plus 15 squared, which is going to give us mhm the square root of 351

Okay. So for this problem. Okay. We want to find factory. Okay. The magnitude is seven and the direction is same mass, vector U. Okay, so let's assume vector V echoes three times k times I Plus four times i times for a nice K times J. Okay. Okay. Is greater than zero and K is in future. Okay. It's a okay. Not being future. Maybe a real number. Okay, so let's see. So the magnitude of me, you go 3K square plus four cases where take the square root, which echoes separate. Okay, that's simply five days. We have 5K. It goes seven. It's okay, echoes 7/5. Okay, so the vector B equals, yeah, three times okay. Three times the mill were five times high Plus four times 7/5 time's jay. When she goes 21/5 times five plus 28/5 times J. Okay, so this is a vector V. Okay.

Okay. So yeah, we have The magnitude of vector v equals seven. And the direction is the same as director of you. So that's fine. Director. We let's assume vector V equals three times kind K times I plus four times K Holmes. J Okay. Okay. is greater than zero K is a real number. So the magnitude of the ecos scared of three k squared plus four k squared, which he calls Samba. So five k squared equals seven. Sorry, five K equals templates. It's okay. You cause 7/5. Okay. So vector V. New course three times k times I Plus four times K Times J. Okay. So which you cause 21/5 times I cause 28/5 times J Okay. Yeah. So this is about to be okay. This is jay.

Foster. We will find Rector. See, on a vector. C is equal toe rector a plus director May I asked Dr A is equal to three. I had minus four dead plus for go ahead. Well, that's actor bees do I had but as three jet minus seven, they had. So this gives us three plus two. I had This is the sum off exit campaigners. Well, as minus for blustery yet this is some of white companies Bolas for money or seven. This is the sum of Z components. So this gives us factor. See equal toe five I id minus You heard minus see dead. Now we have magnitude off. Director, I asked Myrna cuticle toe So get off X component he had X component is five plus. Why component? Hear why? Component is minus one Palazzi component Hair Z component is minus three. This gives us magnitude off distracter equal toe five Mind nine to major. No, In the next part of this problem, we have actor d equals toe two into actor a minus director be so disc use us Rector de equal toe doing director A as rector A's t I had minus for dead plus for go ahead minus director bees do I had well US three jihad minus seven Scared nobody multiplying to with director air. So this gives us two threes are six I had minus two fours. And Jed Well us and you had minus. Do I give minus three Your hair? Well, that's seven. Get nobody reading like drums here. Six in minus tool six. I minus. Do I? That is equal to for I hit minus NJ minus seizure The physical do minus 11. Gerrard Pulis air had mullah seven care This gives us but less 15 scared So this is a position rector Far factor. Do you now magnitude up This victor is equal to so get off So get up X com print Well, us So get off. Why component? But once you get off the component So this use us magnitude of this vector Equal toe 19 So the guys I did a little mistake here I forgot Toe mansion university or yes, we have here Gooners in meter. Yes, we have five meter minus one meter minus three Major. And in this part again, we have rector a in universe a metre. So here four meter minus 11. Major, 15 meter. So this gives us magnitude a worker the equal toe, 19 meter


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