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Problem 1 Easy Difficulty

Match the vector equations in Exercises $1 - 8$ with the graphs $( a ) - ( h )$ given here.
$$
\mathbf { r } ( t ) = t \mathbf { i } + ( 1 - t ) \mathbf { j } , \quad 0 \leq t \leq 1
$$

Answer

graph C

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Video Transcript

Hey, what we want to dio is we're given, um, the vector equation R of t is equal to t I plus one minus t j. Um, where t goes from? 0 to 1 inclusive, and we want to match it up with a graph that represents it in, um, the graph that it is matched to his graph. See, And let's talk about it. Okay, so I have a three dimensional graph. Um, Z axis. Um, I have the why. And of course, X is, um, coming out of the board. Okay. And so, um, if we know that t, um goes from 0 to 1, then X remember eyes for ex Jay's for why? And of course, we have no Z, so we have nothing in the Z you claim. And so if we go from, um, t equals 0 to 1. So if tea is zero, then I have nothing in the extraction, and it's out here in the UAE direction at one. And then when I go toe one as I approach one, then my, um, all of it goes to my X axis, and nothing is on my y axis. And so that's why it is this graph right here. And none of the other graphs listed

University of Central Arkansas
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