Describing the Vector <t,t> for All Real Numbers: Homework Help

[RJLiberator]

Homework Statement

Describe...
t<1,1> where t is all real numbers.

Homework Equations

The Attempt at a Solution

I start by multiplying t to each x and y component.
The resulting vector (field??) is <t,t> where t is all real numbers.

Does this mean that the 'image' is the entire xy plane of all real numbers?

 

[LCKurtz]

Try plotting a few points for various $t$.

 

[RJLiberator]

Oh... brain cramp.
t can be any real number, but it must be only one real number.
So you get a slice through the xy plane.

(1,1)
(2,2)
This is y=x which has a slope of 1.
Correct?

 

[MostlyHarmless]

You could call t a "scalar" meaning it only affects the magnitude of the vector, not it's direction. So what direction is your vector pointing? What's the magnitude?

 

[Nathanael]

This is y=x which has a slope of 1.
Correct?

Yep. All vectors t<1,1> lie on the line y=x