Video: Adding and Subtracting Three Vectors Component-Wise

Given that vector 𝐴 = (9, 5), vector 𝐵 = (−10, 3), and vector 𝐶 = (−3, 6), find vector 𝐴 + vector 𝐵 − vector 𝐶.

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Video Transcript

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.

Now, in order to deal with this kind of question, what we actually do is we deal with the 𝑥- and 𝑦-components separately. 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. So we’re going to start- we’ve got nine cause that’s part of our vector 𝐴. Then, we have plus negative 10 because that’s the 𝑥-component of our vector 𝐵. And then, finally, we have minus negative three and that’s because it says minus 𝐶. So we actually subtract the 𝑥-component of vector 𝐶.

Okay, great, so that’s our 𝑥-components. So let’s move on to our 𝑦-components. 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. So therefore, we subtract the 𝑦-component of vector 𝐶. Okay, fab, so we’ve reached this stage. Now, let’s start to simplify.

So then, we get nine mins 10 and it’s minus 10 because we had plus a negative. So that gives us minus 10 and then plus three. And that’s because if we subtract a negative, it turns into a positive. So that’s our 𝑥-component and then our 𝑦-component as before is five plus three minus six.

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. Well, then, 𝐴 plus 𝐵 minus 𝐶 is going to be equal to two, two. 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.

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