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Math Help - Unit vectors question

  1. #1
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    Unit vectors question

    The following problem was confusing me so any help would be greatly appreciated!

    Find the unit vectors T and N for the given curve at the indicated point.

    r(t) = <t, t^2, t^3> at (1, 1, 1)
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  2. #2
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    Quote Originally Posted by meebo0129 View Post
    The following problem was confusing me so any help would be greatly appreciated!

    Find the unit vectors T and N for the given curve at the indicated point.

    r(t) = <t, t^2, t^3> at (1, 1, 1)
    T and N are tangent and normal vectors, yes?

    I can get you T, but I don't have a specific definition for N: the best I can do is tell you how to find one of an infinite number of normal vectors.

    Anyway, for T:
    \nabla r(t) = <1, 2t, 3t^2>

    At the point (1, 1, 1) we have for an unnormalized T = <1, 2, 3>. This vector has a length of \sqrt{1^2 + 2^2 + 3^3} = \sqrt{14}, so your answer for the unit vector in the direction of T is:

    \frac{<1, 2, 3>}{\sqrt{14}}

    Someone else is going to have to show you how to get N. (I can find a vector perpendicular to T easily enough using T \cdot N = 0, but there will be an infinite number of possible N that can do this. You obviously have a specific property defined that picks out a specific N.)

    -Dan
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  3. #3
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    r(t)=ti+t^{2}j+t^{3}k

    f'(t)=i+2tj+3t^{2}k

    T=\frac{i+2tj+3t^{2}k}{\sqrt{14}}=\frac{1}{\sqrt{1  4}}i+\frac{2}{\sqrt{14}}j+\frac{3}{\sqrt{14}}k

    Now, N(t)=\frac{T'(t)}{||T||}


    If I remember correctly, this is how T and N are found. It's been a while.
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