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Subtracting vectors end-to-end

Watch Sal determine which diagram represents vector subtraction graphically. Created by Sal Khan.

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Video transcript

Voiceover:These are vectors A and B, all right? That's vector A, that's vector B. Which of the following describes a valid way of obtaining vector A minus vector B? So let's look at our choices right over here. Here they just depicted vector B, just like it's depicted here, it's maybe shifted over a little bit. And then over here, they depicted vector A, the negative of vector A, and it looks like they're taking the negative of vector A, and to that they're adding vector B, and then they're claiming that this magenta vector is A minus B. If we ignore what they wrote over here, what they've done is they've added negative A to B. So this is the negative of vector A plus vector B. Or we could think of it as vector B minus vector A. So this one right over here is not right. If we swap the signs, if this was a negative, if we put negative A plus B, then we'd say okay, this is accurate, but they want us to figure out valid ways of obtaining A minus B and this isn't that. This is B minus A. Let's look at the other choice. You have vector A. Let's start at the tail of vector A, get to the head of vector A. Over here we have the tail of the negative of vector B, so they essentially flipped it over when you take the negative of it, and so we're adding negative B to A. If we take the tail of where we started to the head of where we ended, yes, this would be vector A plus negative vector B, which is the same thing as vector A minus vector B, so that one is right. That's a valid way of obtaining vector A minus vector B.