# Finding the angle between 2 vectors problems!

1. Oct 13, 2005

### mr_coffee

The directions say, The helix r1(t) intersects the curve r2(t) at the point (1,0,0). Find the angle of intersection of these curves. Well here is my work, and i'm stuck, how am i suppose to find the dot product of these 2 vectors once i take the derivative? the sin(1) is not a pretty number, and the book gets an asnwer of Pi/2 i think. What did i do wrong? Thanks.
Work:
http://show.imagehosting.us/show/799218/0/nouser_799/T0_-1_799218.jpg

2. Oct 16, 2005

### robphy

(1,0,0) refers to the (x,y,z) coordinates of the intersection point---not the value(s?) of the t-parameter at the intersection point.
From your work... [let P be the intersection]
r1(at P)=(cos t_P, sin t_P, t_P)
r2(at P)=(1+t_P,t_P^2,t_P^3)
and, P=(1,0,0).
So, from the first equation: cos t_P=1 , sin t_P=0, t_P=0,
and from the second equation: ... you can do this part
and finish off the problem.

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