Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
     
  2. jcsd
  3. Jul 3, 2011 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook