Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Baby Do-Carmo's question.

  1. Jul 15, 2011 #1

    MathematicalPhysicist

    User Avatar
    Gold Member

    I have this question: Show that the tangent lines to the curve [tex]\alpha (t)= (3t,2t^2,2t^3)[/tex] make a constant angle with the line y=0 and z=x.

    Now what I have done is, well obviously we have:
    [tex] (1)cos(\gamma (t)) = \frac{\alpha '(t) \cdot v}{|v| |\alpha '(t)|}[/tex] So what I have done is to take the derivative of the RHS in (1) wrt t, where v=(x,0,x).
    My reasoning is that if the derivative is zero then the angle is constant.

    My problem is that I don't get zero, where did I get it wrong?
    :confused::cry:

    Thanks.
     
  2. jcsd
  3. Jul 15, 2011 #2

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If we're supposed to show that the tangent vectors of [itex]\alpha[/itex] make a constant angle with the tangent vectors of that line, then it seems to me that what we have to show is that [tex]\frac{d}{dt}\big(\alpha'(t)\cdot(1,0,1)\big)=0[/tex] for all t. This is obviously not true, so I'm wondering if he might have meant something else. But I don't see how he could have meant something that makes the claim true.
     
  4. Jul 15, 2011 #3

    MathematicalPhysicist

    User Avatar
    Gold Member

    Well, I guess you also have a copy of the book right?

    Anyway, here's a scan for the others.

    question 1.
     

    Attached Files:

  5. Jul 15, 2011 #4

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I don't have a copy of the book, but I don't mind downloading a pdf for purposes like this. I have skimmed the first few pages now. I didn't see any hints that he might have meant something different.
     
  6. Jul 15, 2011 #5

    MathematicalPhysicist

    User Avatar
    Gold Member

    For me 'copy' doesn't necessarily mean hard copy.

    Thanks, anyway.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Baby Do-Carmo's question.
  1. How do I explain this? (Replies: 2)

  2. Manifold Questions (Replies: 25)

  3. Loxodrome question (Replies: 2)

Loading...