1. ## tangent vectors

Show that the curve
γ(t)=(t²-t+1,t³-t)
has exactly one self-intersection point and finnd the two unit tangent vectors (in the direction of increasing t) at this point.

I have found the self intersection. I know that a unit tangent vector is the derivative of each component>But the wording has me a bit confused.What does it mean "in the direction of increasing t at this point"?

2. draw pic

3. Originally Posted by ulysses123
But the wording has me a bit confused.What does it mean "in the direction of increasing t at this point"?
You will naturally compute the unit vector in the direction of t increasing, that is just there to remove all ambiguity. Otherwise you'd have to choose between that vector and its opposite, because they both qualify as unit tangent vectors.

4. when i evaluate the tangent vectors at the values of t for the self intersection i get:

1) (-1,-1)
2)(1,2)

do i normalise this to make it a unit tangent vector? and how do i specify a direction?

how do i know

5. ## tangent vector

i think i figured it out, thanks for your help