Use the figure to find each vector: u - v. Use vector notation...

Question

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

Accepted Answer

Hey, everyone in this problem, we are given a figure that shows two vectors U and V. And we're asked to find U minus V. We're told to express our answer in the form of a comma B with angled brackets around that. OK. So that typical vector notation, we have our figure, we have our two vectors in there and we're gonna come back to that in just a minute. But first, we're gonna look at our answer choices. So option A, we have negative 15 comma nine, option B 15, comma negative nine, option C nine comma three and option D nine comma negative three. So in order to find U minus V first, we're gonna figure out what's you and what's V and we're gonna write them in this form that we want our final answer. OK. So let's start with you. And if we take a look at our graph and we can see that vector use starts at the origin and points out into the plane. And because it starts at the origin and we wanna write the vector in this format that we have, we can write the coordinates of the final point. OK. So if we look at the coordinates of the final point where this arrow for vector U ends, we can see it has an X position of three and A Y position of negative three. And so we can write vector U as three common negative three. With those angled brackets, we're gonna do the same for vector V. When we look at vector V, just like vector U, it starts from the origin, it starts from the origin. Meaning means that we can take the end point of the arrow, the endpoint of the vector, write the coordinates of it, put those angled brackets around it and that's gonna define our vector. So vector V, we can see that it's gonna be at an X value of negative 12 A Y value of six. And so in angled brackets, we have negative 12 comma six for V. We have our two vectors U and V. Now we wanna do the subtraction. So we're gonna do you minus B and this is gonna be three comma negative three minus negative 12 comma six. So we have two vectors, we wanna combine these into one single vector. And in order to do that, we have to remember that more subtracting vectors, we can subtract them component wise. A so we can look at the first components, subtract them, the second component, subtract them and so on and so forth. So let's start what we're gonna start with is the first components So we're gonna take the first component of EU which is three and we're gonna subtract the first component of V negative 12 and we're subtracting them because that's the operation between our two vectors. So we have three minus negative 12. Now we move to our next component, we're gonna take the second component of vector U negative three, subtract the second component of vector V six. So we get negative three minus. And again, we're subtracting them because that's the operation between our vectors. So now we've got this down to a single vector. All we have left to do is simplify each of these components by adding and subtracting and we know how to do that. So the hard part is done and we have three minus negative 12. That's gonna be three plus 12. So we have 15 and then we have negative three minus six. That's gonna give us negative nine. And so our resulting vector U minus V is gonna be 15 common negative nine. If we compare this with the answer choices, we can see that this corresponds with answer choice B. That's it for this one. Thanks everyone for watching. I hope this video helped.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

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Key Concepts

Vector Notation

Vector Subtraction

Graphical Representation of Vectors

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