WEBVTT
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Given that vector 𝐴 is equal to nine, five, vector 𝐵 is equal to negative 10, three, and 𝐶 is equal to negative three, six, find 𝐴 plus 𝐵 minus 𝐶.
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Now, in order to deal with this kind of question, what we actually do is we deal with the 𝑥- and 𝑦-components separately.
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So if we actually have 𝐴 plus 𝐵 minus 𝐶, so we’ve got these three vectors we’re actually dealing with, then first of all what we’re actually gonna deal is our 𝑥-components.
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So we’re going to start- we’ve got nine cause that’s part of our vector 𝐴.
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Then, we have plus negative 10 because that’s the 𝑥-component of our vector 𝐵.
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And then, finally, we have minus negative three and that’s because it says minus 𝐶.
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So we actually subtract the 𝑥-component of vector 𝐶.
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Okay, great, so that’s our 𝑥-components.
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So let’s move on to our 𝑦-components.
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We’re gonna have five plus three because actually three is our 𝑦-component of 𝐵 and then minus six again because we’re subtracting our vector 𝐶.
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So therefore, we subtract the 𝑦-component of vector 𝐶.
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Okay, fab, so we’ve reached this stage.
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Now, let’s start to simplify.
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So then, we get nine mins 10 and it’s minus 10 because we had plus a negative.
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So that gives us minus 10 and then plus three.
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And that’s because if we subtract a negative, it turns into a positive.
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So that’s our 𝑥-component and then our 𝑦-component as before is five plus three minus six.
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So therefore, we can say that given that vector 𝐴 is equal to nine, five, vector 𝐵 is equal to negative 10, three, vector 𝐶 is equal to negative three, six, find 𝐴 plus 𝐵 minus 𝐶.
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Well, then, 𝐴 plus 𝐵 minus 𝐶 is going to be equal to two, two.
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And we found that because nine minus 10 gives us negative one plus three gives us two — so that’s our 𝑥-component — and then five plus three is eight minus six gives us two — that’s our 𝑦-component.