Calc Problem: Find Angle of Intersection Between r1(t) & r2(t) at Origin

[Juntao]

The curves r1(t)=<t,t^2,t^3> and r2(t)=<sin t, sin 2t, t> intersect at the origin. Find their angle (acute) of interesection correct to the nearest degree. (Think! What angle are you trying to locate? Now dn't go off on a tangent.)

So that's the problem.
All I got so far is
r1(t)=t(i)+t^2(j)+t^3(k)
r2(t)=sint(i)+sin 2t(j)+t(k)

Now I'm stuck. I'm not sure where to go now.

 

[StephenPrivitera]

They intersect at the origin at t=0. Now, I only know how to find the angle between two straight lines, so I would disregard the hint and take the derivative. You get r1'(t)=<1,2t,3t^2>=<1,0,0> and r2'(t)=<cost,2cos2t,1>=<1,2,1>.
Now how do you find the angle f between two vectors?
A*B=ABcosf
1=(1)sqrt(6)cosf
f=arccos(sqrt(6)/6)=66 degrees

 

[HallsofIvy]

How is that "disregarding" the hint? The purpose of the hint was to direct you to the tangent lines of the curves.

 

[StephenPrivitera]

I interpreted, "Don't go off on a tangent" to mean "Tangents aren't the way to solve the problem."

 

[Juntao]

Great. My answer matched yours.