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Homework Help: Unit Vector Problem

  1. Jul 11, 2014 #1
    1. The problem statement, all variables and given/known data

    For the equations:

    y1 = 1-x^2

    y2 = x^2 -1

    find the unit tangent vectors to each curve at their point of intersection.

    2. Relevant equations

    d/dx (y1) = -2x

    d/dx (y2) = 2x

    3. The attempt at a solution

    After solving for points of intersection between the two equations (-1,0) & (1, 0), I proceeded to ask the derivative for the slope of these points.

    The slope at x = 1:
    for y1 = -2j

    for y2 = 2j

    The slope at x = -1:
    for y1 = 2j

    for y2 = -2j

    Next, I divided each resultant vector by the magnitude, (2), to obtain the unit vector.

    However, this appears to be incorrect, and I am not sure why.

    Attached is a photo:

    Attached Files:

  2. jcsd
  3. Jul 11, 2014 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Slopes are not vectors. The slopes are 2 and -2 which are scalars. To get a vector along a tangent line of slope 2, figure out a ##\Delta y## and ##\Delta x## such that ##\frac{\Delta y}{\Delta x}=2## and make a unit vector out of ##\Delta x i + \Delta y j##.
  4. Jul 13, 2014 #3
    Ahhh. Yes. Of course. Took me a minute to think about it ^.^
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