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

Question

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

Accepted Answer

Hey, everyone in this problem, a vector is shown in the figure and we're asked to find negative V OK. So we have vector V, we wanna find negative V and we're asked to express our answer in the form of a comma B with those angled brackets around it. OK. So that notation that we use for vectors. So the figure we're given shows vector V and we're gonna come back and look at that in just a minute. And then we have four answer choices all in that notation that we want. So option A negative 15, comma negative 20 option B negative 15, comma 20 option C 20 comma 15 and option D 20 comma negative 15. So in order to find negative V, we first need to know what is V. OK? And we're given that in the figure. So let's write it out in this format that we want our final answer to be in. So we have vector V and if we look at vector V, vector V starts with the origin and points to some point in the plane. Now because it starts to the, at the origin, we can write the vector just as the coordinates of that final point. OK. So if we look at the coordinates of the final point and where the end of the arrow is for vector V, we can see that we have negative 20 comma 15. OK. So we have negative 20 in the X direction 15 in the Y direction. And that's our vector be. Now we wanna find negative V. OK. So negative V is just going to be negative this vector. We just found negative 20 comma 15. And when we have a vector and we're multiplying it by a scalar multiple, which is really what we're doing here. OK. We're kind of multiplying our entire vector by negative one. We can apply that scalar to each component of our vector at each term of our vector. So negative V is going to become negative negative 20. I'm a negative 15 and we've brought that negative inside of our vector brackets and applied it to each term. Mhm All right, negative negative 20. Well, that's just gonna be positive 20 and then we have negative 15. OK? And so negatively that final vector we were looking for is gonna be 20 common negative 15 which corresponds with answer choice D that's it for this one. I hope this video helped. Thanks for watching.

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

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Key Concepts

Vector Notation

Vector Components

Vector Operations

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