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: Is there a formula to find the intersection of a plane and a curve at a given point?

  1. Aug 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the intersection of the x_1x_2 plane and the normal plane to the curve
    x= (cos(t)e_1 + (sin(t))e_2 + (t)e_3

    At the point t = pi/2

    2. Relevant equations

    I have looked everywhere for a formula or an example for this and cannot find one? Can anyone help me as to what I should be looking up, if there is a formula, or a hint on the method I should try.

  2. jcsd
  3. Aug 27, 2007 #2


    User Avatar
    Science Advisor

    First, determine the planes! The tangent vector to cos(t)e_1 + (sin(t))e_2 + (t)e_3
    is -sin(t)e_1+ cos(t)e_2+ e_3 and at pi/2 that is -e_1+ e_3. Of course, at pi/2, the curve goes through the point e_2+(pi/2)e_3.

    The equation of a plane with normal vector -e_1+ e_3 containing point (0,1,pi/2) is, of course, -x_1+ x_3- pi/2= 0 or x_3- x_1= pi/2.

    I assume you know that the equation of the x_1x_2plane is x_3= 0.

    Find all points that satisfy x_3- x_1= pi/2 and x_3= 0. The intersection of two planes is, of course, a line.
  4. Aug 27, 2007 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Why did you look for the formula? Such things are easy to derive for yourself.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook