Finding the angle between two tangent vectors

[navalava]

Homework Statement

Consider the two space curves
r1(t) = <cos(t − 1), t^2 − 1, 2t^4>
r2(s) = <1 + ln s, s^2 − 2s + 1, 2s^2>,
where t and s are two independent real parameters.
Find the cosine of the angle between the tangent vectors of the two curves at the intersection point
(1, 0, 2).

Please show me steps..thank you!

Homework Equations

The Attempt at a Solution

I set cos(t-1)=1 and got t=1.
In the same manner, I got s=1.
But I'm not sure how to get r'(1)...I'd appreciate any help on this!

 

[Dick]

You find a tangent vector to a curve by differentiating the curve, don't you?

 

[navalava]

Yeah, I differentiated it and got r'(1)=<0.841,0,0> and |r'(1)|=0.841, which seems like an odd number...I wanted to confirm that I did it right.
I also got r2'(1)=<1,0,4> and |r2'(1)|=sq.root17.
Is this right? And I just set them over each other to get the tangent vector right?

 

[Dick]

0.841=sin(1). Seems ok so far. You set them 'over each other' to get two unit tangent vectors. Then what?