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Need help with this vector problem -- Thank you

  1. May 14, 2017 #1
    1. The problem statement, all variables and given/known data
    Let L1 be the tangent line to r(t) at the point t = a and let L2 be the tangent line where t = b. Find the equation of the lines L1. Find the equation of the lines L1 and L2 and find the points of intersection.

    r(t) = <f(t), g(t), h(t)>

    *bolded letters are vectors
    2. Relevant equations


    3. The attempt at a solution
    I just wanted to tell you guys my thought process and would you correct me wherever I am wrong. The question has more to it, but the computation would be menial. I'm just having trouble with what vectors to use and all that stuff.

    Steps I would take:
    -r(a) would give me a point on L1 and r(b) would give me a point on L2.
    -find T(t)
    -find T(a) and T(b)
    -for L1, the equation of line would be (f(a), g(a), h(a)) + T(a)t
    -same step for L2 as L1
    -find if there is an intersection by setting the parameters of x,y, and z of the lines equal

    Am I using the correct vector, T(t), for the second step?
     
    Last edited: May 14, 2017
  2. jcsd
  3. May 14, 2017 #2

    BvU

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    Did you forget to tell us what T is ?
    And: do you always expect to find an intersection ?
     
  4. May 14, 2017 #3
    OOps sorry

    the T(t) would be $$\frac {\vec r '(t)} {||\vec r '(t)||}$$
    And no I wouldn't expect to always find an intersection. The lines could be parallel or skew
     
    Last edited: May 14, 2017
  5. May 15, 2017 #4

    BvU

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    In that case: so far, so good :smile: !
     
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