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Math Help - tangent vectors

  1. #1
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    tangent vectors

    Show that the curve
    γ(t)=(t-t+1,t-t)
    has exactly one self-intersection point and finnd the two unit tangent vectors (in the direction of increasing t) at this point.

    I have found the self intersection. I know that a unit tangent vector is the derivative of each component>But the wording has me a bit confused.What does it mean "in the direction of increasing t at this point"?
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  2. #2
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    draw pic
    Attached Thumbnails Attached Thumbnails tangent vectors-test2.png  
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  3. #3
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    Quote Originally Posted by ulysses123 View Post
    But the wording has me a bit confused.What does it mean "in the direction of increasing t at this point"?
    You will naturally compute the unit vector in the direction of t increasing, that is just there to remove all ambiguity. Otherwise you'd have to choose between that vector and its opposite, because they both qualify as unit tangent vectors.
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  4. #4
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    when i evaluate the tangent vectors at the values of t for the self intersection i get:

    1) (-1,-1)
    2)(1,2)

    do i normalise this to make it a unit tangent vector? and how do i specify a direction?

    how do i know
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  5. #5
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    tangent vector

    i think i figured it out, thanks for your help
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