1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Acute Angle between two vector-valued functions

  1. Jul 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Quick question. I need to find cos [tex]\vartheta[/tex], where [tex]\vartheta[/tex] is the angle (acute) between two vector-valued functions (which are tangent lines).


    2. Relevant equations

    I think this is relevant:

    cos[tex]\vartheta[/tex] = (u dot v)/([tex]\left\|[/tex]u|| * [tex]\left\|[/tex]v||)

    3. The attempt at a solution

    Is that the correct equation to use? If so, well, the two equations I'm using both have "t" in them, since they're VVFs. But what do I put in for t? I get the feeling that it's blatantly obvious...Thanks for helping!
     
  2. jcsd
  3. Jul 3, 2009 #2

    zcd

    User Avatar

    Yes, that's the right equation. Dot product is defined as multiplying i, j, and k components of each vector (assuming 3 component vectors) to return a scalar value. |u||v| means multiplying the scalar magnitudes of vector u and v.
     
  4. Jul 3, 2009 #3
    Great, thanks! But when I actually do out the equation, I have all of those "t" variables everywhere (2t+1) - (3t^3), etcetera...what do I substitute in for that?
     
  5. Jul 3, 2009 #4

    zcd

    User Avatar

    That depends on the question. Either it gives you a specific instance for when the two vectors cross or it wants the angle in general form where t is ambiguous.
     
  6. Jul 3, 2009 #5
    The point is (1,1,3). But for u, t = 3, and for v, t = 4. So, do I use one of those t-variables, or go with something else entirely?
     
  7. Jul 4, 2009 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It shouldn't be hard to see that you need to use both of them- one applies to u and the other to v. In fact, instead of using t in both functions, it would be better to use, say, t1 for u and t2 for v. Then set t1= 3, t2= 4.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook