1. Vector Functions

I'm having trouble even knowing where to begin with the following problem. I understand the last part about finding the direction through vector derivatives, but I'm stuck on the first part about how to conver to rectangular coordinates, please help.

In each of the following, find an equation in rectangular coordinates of the graph of the vector function. Sketch the graph and indicate the direction in which it is transversed by considering the behavior of the vector derivative for appropriate valus of the parameter.

F(t)=< 1, 1-t >

2. Re: Vector Functions

You are given that F(t)= <x(t), y(t)> and are asked to write it in "rectangular coordinates". That is, y= f(x), or x= f(y), or some relation involving both x and y.

The first thing I notice is that x is a constant, 1, while y can be any number. What do you think the graph of that looks like?

3. Re: Vector Functions

Sounds to me like it's a vertical line. I'm still having trouble converting it to rectangular coordinates

4. Re: Vector Functions

Nevermind, I just realized that it would be x=1

5. Re: Vector Functions

What about for a problem that doesn't have a fixed variable like:

F=< 2t, 3t+1 >

6. Re: Vector Functions

Originally Posted by dbakeg00
What about for a problem that doesn't have a fixed variable like: F=< 2t, 3t+1 >
$\left\{ \begin{gathered} x = 2t \hfill \\ y = 3t + 1 \hfill \\ \end{gathered} \right.$ solve for $t$ in each case and equate.

7. Re: Vector Functions

Worked like a charm, thanks!