khally92
  • khally92
sketch the vector function r(t)= (-t^2, 4, t ) and indicate with an arrow the orientation of the curve. Anyone please. Thank you.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
First note that the y-coordinate for your vector valued function will always be 4. The significance in that is we can sketch the curve in a plane parallel to the xz-plane, which wouldn't be very complicated at all. So at the time being, let's just focus on the x and z components. \(x=-t^{2}\) \(z = t\) Eliminating the parameter gives us the equation \(x = -z^{2}\) , so a simple parabola. In terms of graphing this, if the flipping around of variables is a little weird, we can always pretend to graph in the xy-plane with functions of x and just flip axes from there. |dw:1450397275335:dw| Plotting \(y = -x^{2}\) is very familiar, so doing that graph and then changing the variables is a nice way to get yourself oriented.
anonymous
  • anonymous
|dw:1450397491465:dw| Seeing this makes it a lot easier to place our curve in the correct direction. Now all we do is transpose this onto some imaginary plane at y = 4 |dw:1450397855134:dw| Not the best drawing, but that's kind of the idea. As for the direction arrows, those can easily be seen by picking 2 or 3 values of increasing t and noticing the coordinate each value gives. You'll see that as t increases, the z-coordinate increases, so I want my arrows to go along the curve towards z increasing.
khally92
  • khally92
Thank you so much you have been of great help. Thank you so so much.

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