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 have two vectors shown in the figure and we're asked to find U plus V. OK. So we're adding those two vectors together. And we're told to express our answer in the form of a comma B and with those arrow shaped brackets around it. So we're looking for both components. Now, if we take a look at the figure, we're given K, we've shown vector U and we're shown vector V. We have four answer choices. Option A negative five comma 30 option B negative 25 comma negative 10, option C negative 30 comma five and option D negative 30 comma negative five. The first thing we wanna do in order to add these vectors, we need to figure out what U is and what V is. OK. So we're gonna take eu and we're gonna look on our graph and we can see that it's at an X coordinate of negative 10, we can write our vector as negative 10 comma and the Y coordinate. OK? We can see this bottom line is negative 25. So each line represents five units. OK? So this is gonna be at negative 20 OK. So U is gonna be negative 10, negative 20 we can do the same for V. It's going to be at an exposition of negative 20 in A Y position of 15. So we can write this as negative 20 comma 15. OK? Because our arrow points from the origin to that point there. OK. So that is how we can write our vector. And now we're just gonna add them up. So you plus B is just going to be equal to negative 10 common, negative 20 plus negative 20 comma 50. Now we're call when we're adding vectors, we can simply add the corresponding components. OK? So we're gonna take the first component of you add it to the first component of V that's gonna give us the first component of the resulting vector. And we're gonna do the same with the second component. And when we do that, it looks like the follow, we're gonna have negative 10 plus negative 20. They were added the first component of you with the first component of the, we're gonna do the same for the second component. OK? So we're gonna add the second component of U to the second component of B. And the result we get is going to be negative 20 plus 15. So this is gonna be our result in vector. And now all we have to do is simplify each of these components which, which is just a matter of adding and subtracting negative 10 plus negative 20. That's gonna give us negative 30 negative 20 plus 15 that gives us negative five. And so U plus V, the resulting vector we were looking for is gonna be negative 30 comma negative five which corresponds with answer choice. D thanks everyone for watching. I hope this video helped see you in the next one.

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

Key Concepts

Vector Addition

Vector Notation

Graphical Representation of Vectors

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