Results 1 to 2 of 2

Math Help - show unit normal vector..

  1. #1
    tnp
    tnp is offline
    Newbie
    Joined
    Sep 2009
    Posts
    2

    show unit normal vector..

    Q)

    Let γ:I->R3 be a regular parameterized curve, with non zero curvature everywhere and arc length s as parameter.

    Let σ(s,v) = γ(s) + r(n(s) cos v + b(s) sin v) [where r is a non zero constant] be a parameterized surface, where n is the normal vector and b is the binormal vector of γ.

    Show that when σ is regular, its unit normal vector is:

    N(s,v) = -(n(s) cos v + b(s) sin v)

    Answer)

    Well, the definition of a unit normal vector is:
    N(s,v) = [∂σ/∂s X ∂σ/∂v]/[|∂σ/∂s X ∂σ/∂v|]

    So then I proceed to evaluate ∂σ/∂s and ∂σ/∂v..

    ∂σ/∂s = ∂γ/∂s + r[(dn/ds)(cos v) + (db/ds)(sinv)]

    and

    ∂σ/∂v = r[-n(s)sin v + b(s)cosv]

    But now I'm wondering, how do I cross product these two if they are not vectors!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    tnp
    tnp is offline
    Newbie
    Joined
    Sep 2009
    Posts
    2
    I'm getting thrown off by the ∂γ/∂s in ∂σ/∂s and also the fact that there is an addition in both ∂σ/∂s and ∂σ/∂v.

    I am aware n and b are the normal and binormal, and thus throwing an scalar constant r and cos/sin in front still makes them vectors, but I don't know how to deal with the additions!

    Would greatly appreciate some advice as to how to tackle them!
    Last edited by tnp; September 12th 2009 at 06:48 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Unit Normal Vector
    Posted in the Calculus Forum
    Replies: 9
    Last Post: June 13th 2011, 06:04 AM
  2. Finding a unit normal vector
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 12th 2010, 10:24 AM
  3. unit normal vector
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 21st 2009, 07:59 AM
  4. Finding Unit Normal Vector
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 19th 2009, 11:37 AM
  5. Unit normal vector function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 2nd 2008, 06:56 PM

Search Tags


/mathhelpforum @mathhelpforum