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Tangent line to a curve in R3

  1. Jul 3, 2011 #1
    So the curve is defined as x-y^2 = 0, z= x . I'm supposed to find the tangent line to the curve. How do I find a slope in R3?
     
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  3. Jul 3, 2011 #2

    SammyS

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    There are infinitely many such tangent lines.
     
  4. Jul 3, 2011 #3
    Oh, right, I meant at the point (1,1,1).
     
  5. Jul 3, 2011 #4

    SammyS

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    How do you write the "equation" of a line in R3?

    Actually, how do you specify a line in R3?
     
  6. Jul 3, 2011 #5
    something like (x1,y1,z1) + t(a,b,c)?
     
  7. Jul 3, 2011 #6

    Dick

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    Ok, can you write the curve (x,y,z) as a function of a single variable? Call that variable 't'.
     
  8. Jul 3, 2011 #7
    Try letting t=x. Then, x=z=t, y=sqrt(t). So, a vector function for your curve should be r(t)= (t) i + (sqrt(t)) j + (t) k (let i, j, k be unit vectors).

    Your point occurs at t=?

    Find the slope of the vector function at that t, and plug into a vector equation for a line.
     
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