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Homework Help: 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


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    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


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    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


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    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.
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