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Numerade Educator

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Problem 4 Easy Difficulty

Match the vector equations with the graphs (a)-(h) given here. (GRAPH CANT COPY)
$$\mathbf{r}(t)=t \mathbf{i}, \quad-1 \leq t \leq 1$$

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Video Transcript

Okay, folks. So in this video, we're gonna take a look at this vector equation, and we want to match this victory equation with one of the grafts from H given here. Okay, So, um, let me just write down the specter equation for you, and then we'll see what happens. So we have this victor valued function are parameter rised by the variable T and its values given by sea multiplied by X hat, which is the same thing as I had. And we are restricting, are there? I mean, we're restricting t from negative oneto one. So the first thing I want you to notice is the fact that there was no Z component. Not only that, there is no white component either. So what that means is that it's gonna be very easy for us to identify the graph because whatever our graph is gonna look like a better not have a Y or z component. It's going to lie on the X axis always. So let's just try and draw it out. So this is the X axis and the Y axis and Z axes. It's not gonna have a Y value or the value is there's gonna be on the X axis. So let's dried out when x zero. I mean, when t zero r zero times I, which is just the origin are is lying and lying at the origin went to you zero. And when she is negative one are is right here on the X axes that values negative one on the X axis. And when tea is one, our goes to here. So, as you can see, this is the graph. And whichever option from eight h that matches this raft is gonna be our answer. And if you look through all of the options, you'll see that at the only option that matches their description is the is the first option, which is a and that's our answer for this video. Thank you until next time.