find-the-distance-between-mathbfxleftbeginarrayc10-3endarrayright-and-mathbfyleftbeginarrayc-1-5enda

Question

Find the distance between $\mathbf{x}=\left[\begin{array}{c}{10} \ {-3}\end{array}ight]$ and $\mathbf{y}=\left[\begin{array}{c}{-1} \ {-5}\end{array}ight]$

Ryan Sander · Accepted Answer

Hello. In this video, we&#x27;re going to compute the distance between the vectors X and Y, where X is given by 10 in the first component. Negative three in the second component. And why is given by negative one in the first component? Negative five in the second component. And so I think it&#x27;s always good to visualize the vectors we&#x27;re trying to compute here. So we have. Let&#x27;s say this first dimension is X one. The second mentions X two like that here, Um and so that means the the point X given by a vector, uh is it can be given by the 0.10 negative three, Which is going to be, ah, somewhere around here. So this will be X and then why is given by the point negative one negative five, which is going to be given by the point around here? Why and then our goal is to compute the distance between these two, which, if you remember from the Pythagorean theorem, can be computed as this distance will call it a B and C see is what we&#x27;re trying to sell for and C is equal to the screwed of a squared plus B squared. And so we&#x27;re actually going to apply that directly here by looking at the differences in the components between these two vectors. So, um, let&#x27;s get back to competing this magnitude. So the difference between two vectors eyes going to be in this case, the distance between X and Y is going to be equal to this. The magnitude of X minus y which, because of the properties of, um, of vector spaces like the one seen like a two dimensional ones in here, uh, X minus Y is equivalent to why minus X and we&#x27;ll see why in just a second. Uh, and so, by definition, uh, this distance is going to be equal to the square root of X one minus why one squared the the first component of acts in the first component of why and then, um, that that different squared plus X two minus y two squared the second component, X minus the second opponent why scored? And the reason why these two are equivalent is because we could equivalently do why one minus X one squared plus or to money sex two squared. And these quantities air the same because the square ensures the squares inside this car creates ensure that these quantities air Always positive. We&#x27;ll just focus on this one on the left eso if we plug our numbers. And now the first component of X is given by 10. 1st component of y is given by negative one. So it&#x27;ll be 10 minus negative, one squared and then the second component of access given by negative three second component wise given my negative five. So we negative three minus negative. Five squared. Okay, which is equal to if we now simplify these, it&#x27;ll be 10 plus one squared plus, uh, negative three plus five squared, which is equal to 11 squared plus two squared, which is spirit of 1 21 plus four, which is the skirt of 1 25. Or if we take a five out if we take move 25. Uh, we converted is this First we&#x27;ll do five times 25 which is equal to the square root of five times the square root of 25 which is equal to square root of five times five or just rewritten. Five squared five. And this is the distance between X and Y. So this see value. And this five squared five, um, are one and the same here. Therefore, the distance between X and Y is going to be given by five Squared five. Thank you.

Ankit Gupta · Answer

we have two points three comma minus like Do you know? Come on, my insulin, The plane. Distance from that, we can make a distance. Equal dinner pre minus. Jiro holds quick bless minus five minus minus. Bless. One holds good. There&#x27;s coming us three miners. Europol&#x27;s got is three square and this is less minus four holes going. So that is You can see that this is night plus 16 to root two in different that this dance is Magnetics.

Ankit Gupta · Answer

one is to lately Goma y minus one directly fights and x two is negative. Five divided by six and why two is three, divided by 10 by using the distance formula should right extra minus X one negative or five divided by six miners. Two. Divided by three It&#x27;s whole display. Let&#x27;s three d word, but minus off one day where we fight its fullest. What should we have? It is New York deal flavor Negative or two times before the heartless six. Oldest left, plus three minus five times stencil to divide. Wait 10 All this which is nine five minus four minus nine. Divided by six. So this 81 by 36 less one buddy under which we can write We can cancel it this three times Well, three times. Why do you say that three times for three times a night? So which is the question? It will take calcium that is 100. So there&#x27;s 9 24 times under 24 times 25 times nine years. 2 to 5 negative off. Sorry. Plus one which is a square toto to 26 way under. So this is the answer. This is their distance

Ankit Gupta · Answer

in point licks a point is a live in coma tree and point with having co ordinate five country. So by distance formula, the length a B we should write a square root off X two that is five minus X wondered, is a living Soldier Square? Bless Why? To minus y when there&#x27;s three minus off three bullets. What this? The square root of minus off six Holy Square plus zero square, which is a square root off statistics that is six units.

Ankit Gupta · Answer

we didn&#x27;t find the distance between two points. The first point is two. Comma to weaken, as in this point is X one comma violent and the second point is minus three comma minus 10. We can assume this point is extra comma white. The distance between two points is denoted as square root. Extra minus x one whole square. Bless. Lie to minus. Live on hold square is equal to after applying the value off x one x two, environment by two will get here minus three minus two. Hold square less minus 10 minus two square. The distance D is equal to squared off minus five square plus minus 12 square. The distance is equal to squared it off. 25 plus 1 44 The distance D is equal to square it off 1 69 as we know that 1 69 inches squared off 13. So we conduct your distance is 13 between two given points

Angela Guo · Answer

We want to find the distance between these two points so the distance is equal to you with a square root off the difference in their excess. So I&#x27;ll be 10 minus five great, plus the difference in their Y values. That&#x27;s negative. 14 minus negative. 11. So that&#x27;s a plus 11 right? So then this is going to equal to square root up. 10 minus 55 by squared is 25 negative. 14 plus 11 is negative. Three and negative three squared is nine, so the distance is going to be the square root of 34.

Problem

Find the distance between $\mathbf{u}=\left[\begi…

Problem 13 Easy Difficulty

Find the distance between $\mathbf{x}=\left[\begin{array}{c}{10} \\ {-3}\end{array}\right]$ and $\mathbf{y}=\left[\begin{array}{c}{-1} \\ {-5}\end{array}\right]$

Answer

5$\sqrt{5}$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

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Joseph L.

Vectors Intro

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5$\sqrt{5}$

Linear Algebra and Its Applications

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David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Catherine R.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications