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General true of false questions about vector function in calc 3

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data
    a. the derivative of a vector function is obtained by differentiating each component function
    b. if r(t) is a differentiable vector function, then d/dt the magnitude of r(t) = the magnitude of r'(t)
    c. the binormal vector is B(t) =N(t)xT(t)
    d. if k(t)=0 for all t, the curve is a straight line
    e. if the magnitude of r(t)=1, then r'(t) is orthogonal to r(t) for all t
    f. different parametrizations of the same curve result in identical tangent vectors at a given point on the curve


    2. Relevant equations



    3. The attempt at a solution
    i think:
    a is T
    b is F
    c i have no idea about what binormal vector is. is it a vector that is orthogonal to both two vectors? if so the cross product would give a vector that is orthogonal to both vectors. so c would be T, i am not quite sure about this one
    d i have no idea
    e i have no idea
    f i think it's T, because although its different parametrizations, the curve is still the same . therefore, the tangent lines at a given point are the same
     
  2. jcsd
  3. Sep 30, 2009 #2

    Mark44

    Staff: Mentor

    Yes, the binormal B is perpendicular to (normal to) the other two vectors.
    What does k(t) represent? Isn't it the curvature? If so, what does it mean to say that k(t) = 0 for all t?
    If |r(t)| = 1, what sort of curve do you have?
     
  4. Oct 2, 2009 #3
    i think i got a circle/sphere, therefore, does that necessarily mean r'(t) is orthogonal to r(t)?

    btw, is my answer to the last question right?
    thank you
     
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