R3 Tangent Line at a Point (1,1,1) for x=t^4, y=t^4, z=t^3

[cybercrypt13]

Homework Statement

Find parametric equations for the tangent line to the curve x= t^4, y= t^4, z=t^3 at the point (1,1,1)

Homework Equations

The Attempt at a Solution

I understand everything about solving this problem with the exception of how to find what t =? to plug in. ie: This equation it equals 1, other problems I see it equals 0 or 2Pi, yet not a single place in 3 books do I see any mention as to how to determine what t is.

What magic are they doing to figure this out?

Thanks,

 

[Dick]

Why don't you understand why t=1 in this problem? Now you are confusing me.

 

[HallsofIvy]

x= t^4= 1, y= t^4= 1, and z= t^3= 1. Is there one value of t that satisfies those equations?