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Match the vector equations in Exercises $1 - 8$ with the graphs $( a ) - ( h )$ given here.

$$

\mathbf { r } ( t ) = t \mathbf { i } + t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 2

$$

graph D

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okay, were given the victory equation. Um, our, uh, t is equal to, um t I plus t j plus t k and T goes from zero Teoh to inclusive. And, um, I am What we're needing to do is match this victory equation with its representative graph. And so we noticed that we have on the X the why and the sea. So I've got a look at my graphs and see which one has something in all three planes, and the only two would be D and E. And but this goes from 0 to 2. And so I noticed that d would be my best option. So let's look, let's look at the graph and discuss why. So here is why this is the and, of course, this is X coming out the board. Um and so, um, win, um, win t zero all of them. Or zero. Um, when tea is to all the X Y coordinates or two. So I notice that if I start off, hear it, too, and then, um, go to to hear and then go up to I end up with a point right here. And so this would be from 0 to 2 in my tea. That would be that vector and so d would be my logical choice

University of Central Arkansas