R1 = < t, 3 - t, 8 + t^2 > and r2 = < 4 - s, s - 1, s^2 >? Find their angle of intersection, θ correct to the

At what point do the curves r1 = < t, 3 - t, 8 + t2 > and r2 = < 4 - s, s - 1, s2 > intersect?
I figured out the points and they are (1,2,9)

However I'm stuck at finding their angle of intersection, θ correct to the nearest degree.

First, find their tangent lines at (1,2,9) <==> t = 1, s = 3.

r₁' = <1, -1, 2t> ==> u = r₁'(1) = <1, -1, 2>.
r₂' = <-1, 1, 2s> ==> v = r₂'(3) = <-1, 1, 6>.

Now, we calculate the angle of intersection via dot product.
u · v = ||u|| ||v|| cos θ
==> 12 = √6 √38 cos θ
==> θ = arccos(3/√57).

I hope this helps!