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 originating from the origin, with u pointing up-right and v pointing down-right on an xy-grid.

Accepted Answer

Hey, everyone in this problem, we're shown two vectors in a figure and we're asked to find vector U minus vector V. We're told to express our answer in the form of a comma B where we have those angled brackets around it to indicate that we have a vector. So we have our figure. OK? And we're showing our vector view and our vector V and we're gonna come back to those in just a minute and then we have four answer choices. OK? All of these are in that format that we want with those angled brackets. Option A is gonna be negative 10 comma 35 option B 10 comma negative 35 option C negative 30 comma negative 35 and option D 30 comma 35. So in order to do this subtraction, the first thing we wanna do is figure out what are these vectors. OK? What is U? And what is V? So let's use the diagram to do that. OK. So we're gonna look at vector U and vector you starts with the origin and points to a point. OK? And because it starts with the origin and we can represent this vector by just looking at the coordinates of that fine point. And so if we look at the final point from vector U, it has an exposition of negative 10 in a wide position of negative 20. And so vector U can be written as negative 10 comma negative 20 we can do the same for vector V. OK. Now vector V again points from the origin to some point in our point because we're starting at that origin, we can represent the vector by the coordinates of that final point. So looking at vector V, it's at an X position of negative 20 A Y position of 15. And so we can write that V is going to be negative 20 comma 15. Now we have our two vectors U and V we wanna subtract. So we have that U minus V. Well, this is just gonna be vector U negative 10 comma negative 20 minus vector V negative 20 comma 15. So we know what it is we want to do. Now, we need to do it and we have to remember here that when we're subtracting vectors and we can subtract them component wise. OK. So we're gonna take the first component of vector U and subtract the first component of vector V. It's gonna give us the first component of our resulting vector and we did the same for the second component. OK. So we're gonna do this component wise. So let's start and we're gonna start with the first component. So we're gonna take negative 10, the first component of U and we're gonna subtract negative 20 the first component of V. And that's gonna give us negative 10 minus negative 20. And we're gonna do the same for the second component, negative 20 minus 15. We're gonna get the second component of our resulting vector negative 20 minus 15. OK. So now we have this all into one vector. All it's left to do is simplify each of those components, which is just a matter of adding and subtracting. We know how to do that. So we have negative 10 minus negative 20. That's gonna give us negative 10 plus 20. And so we end up with 10 for the first component. So we have negative 20 minus 15. That's gonna be negative 35. And so our resulting vector U minus V is going to be equal to 10 comma negative 35. If we compare to the answer choices we were given, we can see that this matches with answer choice B 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 Subtraction

Vector Notation

Graphical Representation of Vectors

Watch next