Video: Subtracting Two Vectors Component-Wise

Given that vector 𝐴 = (1, 9) and vector 𝐡 = (βˆ’4, 1), find vector 𝐴 βˆ’ vector 𝐡.

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Video Transcript

Given that vector 𝐴 equals one, nine and vector 𝐡 equals negative four, one, find 𝐴 minus 𝐡.

So in order to actually solve this, what we’re actually going to do is deal with our π‘₯- and 𝑦-components separately. So when we actually subtract 𝐡 from 𝐴 β€” so our vector 𝐡 from our vector 𝐴 β€” we’re going to deal with our π‘₯-coordinates and then we’re going to move on to deal with our 𝑦-coordinates. So with that in mind, we’re gonna have 𝐴 minus 𝐡 β€” so vector 𝐴 minus vector 𝐡 β€” is equal to one because that’s the π‘₯-component of our vector 𝐴 minus negative four and that’s because that’s the π‘₯-component of our vector 𝐡.

So now we move on to our 𝑦-components. And we have nine minus one because one is actually the 𝑦-component of our vector 𝐡. Okay, great, so our next stage is to actually simplify. So then, our next line in working is that vector 𝐴 minus vector 𝐡 is equal to one plus four as our π‘₯-component. And we got one plus four because we had minus a negative and if you minus a negative, this turns positive. And then, we moved on to our 𝑦-component and this stays the same at this point, which is just nine minus one.

So therefore, we can say that given that our vector 𝐴 is one, nine and that vector 𝐡 is equal to negative four, one, vector 𝐴 minus vector 𝐡 is gonna be equal to five, eight. And we got that because we had one plus four as our π‘₯-component that gives us five and nine minus one as our 𝑦-component which gives us eight.

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