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

Question

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

Accepted Answer

Hey, everyone in this problem, we're given a vector shown in a figure and we're asked to find the negative of that vector. OK. So this vector is labeled V. We wanna find negative V. We're told to express our answer in the form of a comma B with angled brackets around it, that typical vector notation that we see. So we have our figure, we have vector V and we're gonna come back to it in just a minute. But first, let's take a look at our answer. Choices. There are four of them. Option A six comma negative 12, option B negative three, comma three, option C 12 comma negative six and option D negative 12 comma six. Now, the first thing we need to do in order to figure out negative V is first figure out what's V. Hey, we're given it in our diagram, but we want to write it in this notation that we want our final answer in. So let's take a look that to me and vector V starts from the origin and then points up into the left. OK? Because the vector starts at the origin and we wanna write it in this notation that we're given what we can do is write the coordinates of the final point of this vector. So we look at the point where this vector points to, OK. The end of the arrow, we write the coordinates, we put those angled brackets around it. And because the vector started at the origin, that is going to represent the vector. So if we look at the X value of the point where the arrow ends, it's gonna be at negative 12 and the Y value is gonna be at positive six. So our vector V is going to be equal to an angled bracket negative 12 comma six. OK. So that's vector V and now we wanna find negative V. So negative V. Well, that's just gonna be negative this vector negative 12 comma six. Now we have the negative in front. This is like multiplying by a scale or multiple and it's like we're multiplying by negative one. And when we multiply our vector by a scalar, OK, that scalar is gonna apply to each component of our vector. And so we're gonna take our negative and we're gonna apply it to the first component negative 12. And now we're gonna apply it to the second component six. OK? So they're both gonna get multiplied by that negative. When we do that, our vector is gonna look like this negative negative 12 com negative six. OK? So that vector or that negative sorry went into each of those terms. Now we just need to simplify, we're down to our single vector. We've got that negative inside of our vector. It's just a matter of simplifying negative negative 12, that's gonna give us a positive. So we end up with 12 comma negative six and that is our final vector that is negative V. OK? And if you compare it to the original vector V, what you can see is just that the signs of each component switch. OK. That's really what we've done. We brought that negative into each of those terms and it swapped the signs comparing to our answer traces, we can see that this matches with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

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

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Key Concepts

Vector Notation

Vector Components

Vector Operations

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