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Compute the quantity using the vectors u =and v =()((Simplify your answers....

Question

Compute the quantity using the vectors u =and v =()((Simplify your answers.

Compute the quantity using the vectors u = and v = () ( (Simplify your answers.



Answers

Use the vectors $\mathbf{u}=\langle\mathbf{2}, \mathbf{2}\rangle, \quad \mathbf{v}=\langle-\mathbf{3}, \mathbf{4}\rangle, \quad$ and $\mathbf{w}=\langle\mathbf{1},-\mathbf{4}\rangle$ to find the indicated quantity. State whether the result is a vector or a scalar. $$(\mathbf{u} \cdot 2 \mathbf{v}) \mathbf{w}$$

Suppose I have three different vectors. U. V. And W. And I see here that I'm doing the dot product of U. Times to be what is T. V. Well, two V. Whenever I'm multiplying two outside of vector are multiplying each component of the vector by that number. So two people end up being to 10% of three negative 62 times 48. And it's still have a vector is my answer. So now doing the dot product, you dot to be dot product and multiply the first two components together, plus the next two components together. This will end up with multiple before I add negative 12 plus 16 and negative 12 plus 16 is four. Since I only did adopt product first I multiplied by two V. Which resulted in a vector. But then I did a dot product of two vectors, which results in a number. So my answer is a scalar.

Well we have a number five and that's going to write each victor as a combination of New Victor and Victor from Question # three. And so in question number three, let us write down your electricity you back there. We should be just writing down over here. You have uh but having magnitude of magnitude like this, you lift it and directive was like this, this is a director. So in our case in Poland # five, the Victoria is having to fool to go and fight the victor is if you start from here 1234 here four boxes and then five boxes up. 1, 2, 3, 4 5 12345 boxes up. So victory is like, okay This is the victory which is being given in Poland # five. Okay. Okay. And so we have to use uh you victor and victor to find the combination to write the combination of. Are you victor and be a v victor? To get to the value of the director. Are vector in power number five. Let us say w vector. So If we look about look at Victor it is -4012. Right? five. In component form. If you look at you victor it is one comma one. And if you look at me but it is Equal to -1, comma two. We need to combine these victors to get those values. Solar is multiply this victory by a this victory by B. So that after combining these vectors we get vector no, according to the property we should. Right? Uh W vector equal to you return a you victor. Let's be the Director. Okay, so w victories minus four comma. Right. And you corrected Bliss au victor. Place the director will be uh minus B, comma A place to be. Okay, so let us compare this a minus B will become equal to minus four, and A place to be will be equal to five. Let us right down here, A place to be equal to five. subtract minus three, be equal to minus nine, so B will be equal to three. B is three. From here, it will be equal to minus four plus B. The uh -1. The combination will be w vector equal to minus you. Like to bless three. Re victor. Thank you. Yeah.

We have a problem # three. And this is the combination. Uh we have problem number 16. In this there is a vector which is being given so that I support that victory. W in component form this will be 12345 five comma 123 minus three. We need to write the blue as a combination of au director and give it give it From question # three. Well, so From question # three, the component form of you victor. It will be equal to one comma one and be better. Will be equal to minus one, comma two. So let us plug in here. It will become five comma -3 equal to A one, comma 1 Plus B -1, comma two. Five comma minus three. Equal to A -7. Camera. A place to be. Let us compare X component. The tax, component by component by component five. Equal to a -B and a place. OK -3.2. A place to be bless minus minus eight equal to minus three D. So B will be equal to -8 x three. King. Food by criminals. Yes, be equal to minus eight x three. So from here it will be equal to five Plus B, so five eight x 3, which is seven x 3. So W will be seven x 3. UK. You victor -8 x three. V. Victor. Thank you so much. This is a combination.

Okay. So from the graph we can see the vector you you're close to. Okay. Mhm -88. Right? And the vector V. Equals 248. Yeah. So now let's find you. Plus fee. So you plus fee it goes to -8. 8 plus 4. 8 equals two -4 16. Okay. And for B u minus me equals two -88 by this 48. So this equals 2- to health zero. For C This equals 2 -2 of the victory you which he goes to minus of by this uh 88, Which goes to 8 -8.


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