5

For the following vector; convert from x and y coordinates to magnitude ad direction 5, y = 8Submit Question...

Question

For the following vector; convert from x and y coordinates to magnitude ad direction 5, y = 8Submit Question

For the following vector; convert from x and y coordinates to magnitude ad direction 5, y = 8 Submit Question



Answers

Find a vector in the direction of vector $5 \hat{i}-\hat{j}+2 \hat{k}$ which has magnitude 8 units.

We have the number 18 and this we need to find the magnitude and direction of the vector, which is in component form over here. So the best way to deal with this problem is to draw the point eight Common -4. So somewhere here, eight comma minus four, you can say it is in fourth quarter and this line will be its length. That is the magnitude of director and this is the direction, this is alpha. So magnitude will be getting first. My nature will be equal to X component whole square, Let's y component old square. So this is 64 plus 16 and the lady The Route 18, which is it's fine. In line 4 4 and direction direction tita will be equal to this. Complete angle is two pi. That is 360 degrees minus alpha. So 360° 10. Universe four by eight. That actually will be the under 16 minus then in verse four by eight, 2.5, He ended 33 points for three degrees 44 or 45 Brigades. This is the direction And this is the many Children. Thank you

We have problem number 17 and this we need to find the magnitude and direction of two comma minus five. This is a vector in component farms best way is to draw it. So took two comma minus five will be somewhere in fourth quadrant. Okay, okay. And this itself. This length is magnitude and direction will be this angle theater if they sell for. So, first of all, the magnitude will be to a square place -5 was quite under route. So four plus 25, 29 and zero A 29 five point the age frank and direction. I think that will be equal to uh this complete angle is to buy that is 360 degree minus alpha. So 360° canon. Worse fight by two king. So You have the 60° In verse 2.5 291 Point 801 debate. Mhm. You see the magnitude and they say the direction. Thank you.

Okay. So we want to find the picture. We okay. Which has magnitude of eight. And the direction is the same as the direction of factory. You okay. Let's assume the vector V equals five times K. and six times K. Okay. Yeah. Okay. It belongs to the teacher and K is greater than zero. Okay, So let's find the magnitude of this vector B. Okay. Yeah. Okay. So we have This equals eight. Okay. Let's simplify. So we have square root of 25 K squared plus 16 K square because eight Uh sorry, 36, not 16. Yeah. So squared off 61 case bird. It was eight Square the 61 times k equals eight. Okay. Okay. Equals eight over square top 61. So let her we you close. Okay. Five times eight over square of 61 comma six times Yeah. A over square to 61. Okay. Which he calls 40 over squared 61. 48 over squared of 61. Okay, so this just vector V. Or you can you can uh rationalize the denominator. So we have 40 times square to 61. Over 61. 48 times to go under 61. Over 61. Okay.

Hello. I hope you're doing well today. And, um, today we're gonna be talking about vectors. So if we're given a vector, um, on the initial point of the vector as well as the position rector, we should be able to find the terminal point in the magnitude of the vector. Okay, so we're getting the initial point. Negative. Korean? I could've five. Let's go ahead and just mark that on our grass and red. Um, negative three native guys should get those right there. Okay. A man were also given the position. Vector age. Negative, too. So I'm gonna go ahead and draw that injury. You are just right that I ate native to. So basically, um, what this is telling us is that from the initial point, we're going up eight and left. Ah, left negative to or left to basically, um, So I'm gonna go ahead and draw that so it could go up age from negative five. We should end up at three. And then if we go left to we should end up right there. So I'm gonna go ahead and write everything else, Okay? Um, actually, that leaves the gap, Intergraph. So I'll just draw it right here. Okay. Eso Now we have our initial point which was given to us and our terminal Korean. So we can just go ahead and connect the two and draw the arrow. Okay, so there's director, and now all that's left to do is to find the manager. And for that, we actually don't even need anything other than this right here. So to find the man intrude, what we do is use the distance formula, which is a screw of each component squared and added so eight squared, plus negative two squared. Um, it gives us a square root of 64 plus horror, which is equal to the square root of 68 which is approximately. Put that into my calculator X point to close. So that is a magnitude of director. Um, I hope that's helpful. And I hope you have a great day. Thanks for listening.


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