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Question

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Answers

$37-40$ Find $|\mathbf{u}|,|\mathbf{v}|,|2 \mathbf{u}|,\left|\frac{1}{2} \mathbf{v}\right|,|\mathbf{u}+\mathbf{v}|,|\mathbf{u}-\mathbf{v}|,$ and $|\mathbf{u}|-|\mathbf{v}|$
$$
\mathbf{u}=2 \mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}
$$

Hello and welcome to this video solution of numerous. Here we are given a link comprehension. So here in statement one were given that and iron or a on roasting with sodium carbonate and lying in the presence of air gives to compound PNC. And you're from option the second part the solution be in concentrated. It's alan reaction with production furrows and it gives a blue color on precipitated of compound their cost solution of C. On treatment with considerate statistical gives a yellow colored compound E. And the compound even treat it with a seal gives an orange red compound F. Which is used as an ox raise anything. So you have to make certain predictions to come into the solution. So let me show you how it's made. So first of all we take for if he oh she had to poetry thus eight and a two freedom global neck And with air that is given seven or 2 good line gives you to a free two or three that's eight the name so Seattle four. That's it. It's a frustration. Next we have if we two or three reacting with concentrate sales that is given gives you who official three Last three H 2. Right now this official tree reacts with who before if he 10 6 that is protection fellow sign a great this gives you the blue solution pushing blue solution of if the four if he CN six whole trade plus 12 cases. Mm Next From three we have two any he wanted to see our well for That's 8/10 of food gives you we need to the odd 47 is the yellow color solution. Greatness in A. Two so four. That's it too. No you have in A to see our two or seven. Okay, last case here is the orange color substance of people pr two or seven that's 2010. So this is the so let us state what is A what is B. The first we have me is If you see a 23, this is a Next we have every two or 3 SCB or Yes. So this suits also be ready And in in 204 this is C. Right BNC. That is mentioned. Yes. Now this pushing blue books. Mhm. Yeah. Yeah. Whoa it is. Mhm. Okay. To see again this election with the this one your local er this is E and we have orange. What are some common? It does if Yeah. Right. I hope this is clear to you and have a very good rest of the day. Thank you.

We have vectors. U, which is negative. Two plus two U. J two i plus three j and we also have V, which is I minus two j. So these factors and compose converted into component form gives us negative 23 just by looking. The coefficients and V is one. It's that this is I I minus two j one negative too. So the nine itude is found by finding the square root of the sum of the squares off the components. So negative two squared is four plus three squared, which is nine gives us skin is five. So the magnitude of you of after you is five or scare. Sorry. This would be 13 actually Screw of 13 and then for V the magnitude of e, we have one plus four. So this Aziz equal to square root of five and then for to you to two times you we get negative. Four six. I multiplied the components each of the components of you with two, and we get 36 plus 16. So to you is scared of 52. And the magnitude of 1/2 fee is 0.5 negative one, and we're gonna do the same thing. Square root of 0.5 squared plus one plus one square, which is just one. Um, this is equal to square it of five for its And the next one we want to find issue, plus the magnitude of you plus feet. So this one is, um U Plus V is negative one one, which means that our magnitude is scared of to and u minus fee is is us negative three five making this square root of 25 plus nine, which is equal to squared of 34. Finally, the magnitude of U minus magnitude of the well, we really know what the magnitude of us squared of their team. Gonna subtract the magnitude of you which is great of five, and this is equal to and plug this into a calculator, or we can actually leave it as it ist in this form.

We're trying to find the angle state of between vectors U and V. We can start out by knowing that co sign of data is equal to you dot v over absolute value of you dot Absar value v magnitude. And we can first start by working on what you dot visas. And if we already know you envy, we can just start right away with one that'll Kirby there one dot for plus two o plus negative to negative three and that is four plus zero plus 6 +74 and six would be 10. Next step we have our magnitude of you is equal to root of one squared plus two squared plus negative two squared just going to be able to 48 and nine and Route nine is equal to three. Then we have or absolute value the which is going to be four squared. We can ignore zero plus a negative three squared. Yes, we have 16 and nine, which is route 25. Nice clean numbers here That's equal to five. So now we know that co sign of data is equal to 10/3 times five and then we can know that data is equal to inverse co sign of 10/15 and 10/15 is the same as to over three, and then the inverse co sign of two of her three as a decree would be 48.19 degrees.

We're going to find the component forms um going from .12.2. So each time we'll be taking our second point and subtracting the corresponding component from the first. So for our first factor we would consider that we do negative four minus negative six and a negative one minus negative. To notice those minus negatives end up being adding. So we get 2 to 1. So it can either be written with the brackets or we can write it in R I. J form which would be to I plus one J. And I don't have to write the one. If you just see the J. You know that there's a one there Kate. Now our next vector notice every single time we're going to be doing negative 1 0. Well this is already in kind of its component form because its origination is at zero. So we can really write our vector as just the negative 161 And if we write an I. J and k notation we could have a negative I plus six, J plus K. Now our third we'll have to a nine minus four A one minus one and a negative three minus negative three. So in the end I have no J and K. So in the notation that I've already written with brackets you would actually place in a zero where there are, you know, um no components of that form. But when you go to write it in I. J and K, you just write that as five A. If you don't write the J and K component, then it's known that those are zero.


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