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.

Graph showing vectors u and v on an xy-plane with arrows from origin to points (-4,-4) and (4,4) respectively.

Accepted Answer

Hey, everyone in this problem, we're given two vectors in the figure U and V. And we're asked to find U plus V. We're told to express our answer in the form of a comma B with angled brackets around there to indicate that this is a vector. So we have our figure, we're giving those two vectors U and V and we're gonna come back to those in just a minute. But first, let's take a look at the answer. Choices, all of them are in that form that we want. So we have option A negative 15 comma negative three, option B negative 15 comma three, option C nine, comma negative three and option D negative nine comma three. So we wanna find U plus V. Let's first figure out what's you, what's V and we're gonna write them in this format that we want our final answer. And so let's look at vector U. And if we take a look at vector U vector U points from the origin, it at some point in the plane, and because it starts at the origin, OK, we can represent that vector by writing the coordinate of the final point OK. So if we take a look at you, we take a look at this final point, we can see that it has an X value of three and A Y value of negative three. So we can write the vector with angled brackets as three comma negative three. Now we can do the exact same thing for V. So we look at V and V also starts from the origin and points out into the plane. And because it starts at the origin, we can just take the coordinates of that final point. So if we take a look at this final point and we can see that it has an X value of negative 12 and A Y value of six. So we can write V with angled brackets as negative 12 comma six. Hey, so we know you, we know V and now we wanna act, what we want is U plus B and this is gonna be equal to three comma negative three plus negative 12 comma six. They were adding those two vectors that we found. Now we need to combine these into a single vector. And what we have to do here is to remember that when we add vectors, we can add them component wise. So what that means is we can take the first component of you add to the first component of V. That's gonna give us the first component of our resulting vector. And we can do the same with the second component, the second component of U plus the second component of V is gonna give us the second component of our resulting vector. So let's write this all up. OK. For our first component, we're looking at the green and we're taking the first component of U three, we're adding because that's the operation between our vectors. The first component of V negative 12, then we do the same for the second component. We take the second component from vector U negative three we add because that's the operation between our vectors. The second component of vector V six. And this is the final resulting vector. And the only thing left to do is simplify each of those components just as a matter of adding and subtracting. So we have three plus negative 12. That's gonna be three minus 12 which gives us negative nine and then we have negative three plus six. That's gonna give us positive three. And so our final vector U plus B is going to be negative nine comma three which corresponds with answer choice D. That's it for this one. Thanks everyone for watching. See you in the next video.

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

Key Concepts

Vector Addition

Vector Notation

Component-wise Addition of Vectors

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