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

Welcome back. I am so glad you're here. We're told two vectors are shown in the figure, find vector U minus vector V express your answer in the form A B and we're given a figure, we have a vertical Y axis, a horizontal X axis. They come together at the origin in the middle. And then a coordinate plane is marked off with the grid and both axes have their grids marked off in increments of three. We have a vector U which is a position vector with its initial point at the origin and it extends down into the third quadrant. And then we have another vector V also a position vector with its initial point at the origin that extends up into the first quadrant. For our answer choices. Our first answer choice is a negative three com excuse me, negative six comma three answer choice B negative six, comma negative three answer choice C negative 12, negative 21 and answer choice D negative 1221. All right. So if we are finding vector U minus vector V, we can see from our coordinate plane here. We can identify the horizontal and vertical components for both of our vectors. So for vector U, that's going to be a comma B and then we'll subtract vector V's horizontal and vertical components which will be C comma D. And then once we've identified both the horizontal and vertical components that will equal, we'll take the horizontal components minus each other. A minus C, the vertical components subtracted from each other B minus D. So let's identify our horizontal and vertical components. For vector U, we can see that from the initial point at the origin, it goes to the left nine unit. So that's a negative nine. And for the vertical component, it goes down nine units. That's also a negative nine. Now, for our vector V from the origin that goes to the right three units, that's a positive three for the horizontal component and then it goes up 12 units. So that's a positive 12 for the vertical component. And now we've identified our ABC and D, we can just plug these in. So A minus C is negative 12 minus three and B minus D is negative 12 minus N. Excuse me, I'm saying it wrong again, negative nine minus 12. And now we just need to simplify that. So for vector U minus vector V for the horizontal component that is negative nine minus three, which is negative 12 comma for the vertical component that is negative nine minus 12, which is a negative 21. So we look at our answer choices for negative 12, negative 21. And that matches with answer choice c well done. We'll catch you on the next one.

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

Geometric Interpretation of Vectors

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