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Comparing the components of vectors

Sal figures out which vectors have the same x-component given the graphs of 4 different vectors.

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Video transcript

- We're asked, "Which of the following vectors have "the same x component as vector a?" And they tell us to "Select all that apply" This is vector a right over here and we only have to concern ourselves with the x component. That's what they're asking us about. Let's think about what it's x component is. We're starting at this point right over here, which has an x value of negative two and we're going from x equals negative two to x is equal to negative five. Our change in x, another way to think about it, our x component. We're going from negative two to negative five. Our x value goes down by three. Our change in x is equal to negative three. That would also be the x component of vector a. We could say that vector a is equal to, it's x component is negative three. We're not concerning ourselves with our y component but we see that our y goes up by one. So it's negative three comma one but we just care about our x component. Let's think about what other vectors here have an x component of negative three. That, if we start at our initial point and go to the terminal point, our x value has gone down by three. We're gonna start with vector b here. And let's see, if we start there our x value is three at our initial point, our starting point for that vector. Then, to go to the x value of the terminal point we once again went down by three. This has the same x component. Vector b is going to be negative three comma something. I will select that one. Let's think about vector c. Vector c starts here at x equals negative 4 and then it ends at x equals negative one. It's x component is going to look, one way to think about it, our change in x is going to look like this. You might be tempted to say this is the same thing. It has a length of three but notice, we're not going three to the left, the way that we did in vector a or in vector b. We're going three to the right. Here our change in x is positive three and so vector c is going to be positive three comma something. It's not gonna be vector c. Now let's look at vector d. Vector d starts over here, it's x value is negative six and we're going from x equals negative six to x equals negative nine. Once again we have gone down. Our change in x is negative three. That has the same x component. If I were to say vector d I would say it's negative three comma something. I haven't figured out what these are but I don't need to for this problem. So vector d also has the same x component, an x component of negative three and we're done.