sketch the vector function r(t)= (-t^2, 4, t ) and indicate with an arrow the orientation of the curve.

Anyone please.

Thank you.

Question

sketch the vector function r(t)= (-t^2, 4, t ) and indicate with an arrow the orientation of the curve.

Anyone please.

Thank you.

anonymous · Answer

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.