About this video
The video asks which vectors have the same x component as vector a. Vector a goes from x = -2 to x = -5, so its x component is -3. Vectors b (from x = 3, down by 3) and d (from -6 to -9) also have x component -3, while c (from -4 to -1) has +3 and does not match.
You'll be able to
- find the x component of a vector from a graph.
- explain why the sign of a component matters.
- compare components of vectors that start in different places.
Key words
- x component
- The change in x from a vector's initial point to its terminal point.
- initial point
- Where a vector starts.
- terminal point
- Where a vector ends.
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.
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