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. Everyone. In this problem, vectors U and V are shown in the figure we want to find U minus V and express our answer in the form A B for our answer choices A is negative 48 6. B is zero, negative 30 C is 48 negative six and D is 36. Now, in this problem, we want to find U minus V. In other words, we want to subtract both vectors from each other. But before we can subtract them, we need to figure out what the vectors are. So let's go to our graph. Now if you notice on our graph on the X axis, each unit goes up by six, so it's 6, 1218, 24 and so on. Likewise on or Y axis notice that each unit increases by two. In other words, we have two and then four. And in the negative direction, we have negative two, negative four and so on and so on. So starting with vector U, OK. Victor you, if we look at Victor you, if we count in the X direction, we'd go negative 12, negative 18, negative 24. So its X value is negative 24. OK? And its Y value starts coming from negative eight, negative 10, negative 12. So its X value is negative 12. Likewise for V game notice that its X value is 24. So if we come down here, its X value is 24 and its Y value would counting from negative 12, we have negative 14, negative 16, negative 18. OK. So V would be equal to 24 negative 18. Now that we have the values of U and V, we can go ahead and subtract because now this means that to subtract the vectors, we subtract the respective components. In other words, U minus V would be equal to negative 24 minus 24. The X components of U and V and the difference between the Y components of U and V that is negative 12 minus negative 18. Now here negative 24 minus 24 equals negative 48 and negative 12 minus negative 18 is actually negative 12 plus 18. Because when we subtract a negative, it becomes positive and negative 12 plus 18 equals positive six. Therefore, U minus V equals negative 48 and positive six. If we look at our answer choices, that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

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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