# Video: Subtracting Two Vectors Component-Wise

Given that vector 𝐴 = (1, 9) and vector 𝐵 = (−4, 1), find vector 𝐴 − vector 𝐵.

01:27

### Video Transcript

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

So in order to actually solve this, what we’re actually going to do is deal with our 𝑥- and 𝑦-components separately. So when we actually subtract 𝐵 from 𝐴 — so our vector 𝐵 from our vector 𝐴 — we’re going to deal with our 𝑥-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 𝐵 — so vector 𝐴 minus vector 𝐵 — is equal to one because that’s the 𝑥-component of our vector 𝐴 minus negative four and that’s because that’s the 𝑥-component of our vector 𝐵.

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 𝐵. Okay, great, so our next stage is to actually simplify. So then, our next line in working is that vector 𝐴 minus vector 𝐵 is equal to one plus four as our 𝑥-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 𝐵 is equal to negative four, one, vector 𝐴 minus vector 𝐵 is gonna be equal to five, eight. And we got that because we had one plus four as our 𝑥-component that gives us five and nine minus one as our 𝑦-component which gives us eight.