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're given a figure that shows two vectors U and V. And we're asked to find U plus V and we're told to express our answer in the form of a comma B with angled brackets around it. OK. That typical vector notation, if we're writing out the components, now we're given our figure with our two vectors and we're gonna come back to that in just a minute. We have four answer choices. Option, a negative 30 comma zero, option B zero, comma negative 30 option C 30 comma zero and option D zero, comma 30. So let's start. And in order to figure out U plus V, we first need to figure out what each of these vectors U and V are on their own. And we're gonna write them out in this notation that we want our final answer. So starting with vector you and vector use starts at the origin. OK. So it points from the origin to some point in the plane which were shown because it starts from the origin, we can write the vector just as the coordinates of this final point that the vector points to. OK. Because we're starting at the origin that represents our vector. So if we take a look at this point where vector U ends, OK? We have um X each box in the X direction is six units. OK? So we have negative 30 to the left. So we're gonna be at negative 24 in the X direction and in the Y direction OK. Each box represents two. So we're gonna be at negative 12. OK? So vector U is going to be negative 24 comma negative 12. And we can do the same for vector V. They know vector V also starts at the origin and points to a point in the plane because we start at the origin, we can write the coordinates of that final point and that will represent our vector. OK. Now, for vector V we have positive 24 in the X direction and negative 18 in the Y direction. OK? So 24 comma negative 18, that's vector V. And now we wanna find U plus V. OK? So we're gonna take U plus V and this is just gonna be negative 24 comma negative 12 plus 24 comma negative 18. And we have to remember here that when we add vectors, we add them component wise. OK? So we take the first components, add them, take the second components, add them and so on and so forth. And so in this problem, we have two components. OK? So we're gonna take the first component of vector U and add it to the first component of vector V. And when we do that, we're gonna have negative 24 plus 24 as the first component of our resulting vector, then we're gonna do the same for the second components. So we have negative 12 plus negative 18. And that's gonna give us the second component of our resulting vector negative 12 plus negative 18. OK. So now we've simplified this all the way to a single vector. All that's left to do is simplify each of these components, which is just a matter of adding and subtracting. We know how to do that. So let's look, we have negative 24 plus 24. That's just gonna give it zero and then we have negative 12 plus negative 18 and that's gonna be negative 12 minus 18 which gives us negative 30. And so U plus V that resulting vector we were looking for is gonna be zero comma negative 30 which corresponds with answer choice. B 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.
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Key Concepts

Vector Addition

Vector Notation

Graphical Representation of Vectors

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