# Video: Subtracting Two Vectors Component-Wise

Given that vector π΄ = (1, 9) and vector π΅ = (β4, 1), find vector π΄ β vector π΅.

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### Video Transcript

Given that vector π΄ equals one, nine and vector π΅ equals negative four, one, find π΄ minus π΅.

So in order to actually solve this, what weβre actually going to do is deal with our π₯- and π¦-components separately. So when we actually subtract π΅ from π΄ β so our vector π΅ from our vector π΄ β weβre going to deal with our π₯-coordinates and then weβre going to move on to deal with our π¦-coordinates. So with that in mind, weβre gonna have π΄ minus π΅ β so vector π΄ minus vector π΅ β is equal to one because thatβs the π₯-component of our vector π΄ minus negative four and thatβs because thatβs the π₯-component of our vector π΅.

So now we move on to our π¦-components. And we have nine minus one because one is actually the π¦-component of our vector π΅. Okay, great, so our next stage is to actually simplify. So then, our next line in working is that vector π΄ minus vector π΅ 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 π¦-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 π΄ is one, nine and that vector π΅ is equal to negative four, one, vector π΄ minus vector π΅ 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 π¦-component which gives us eight.