1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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: Hyperboloid problem

  1. Jan 28, 2007 #1
    1. The problem statement, all variables and given/known data
    Hello, can someone tell me where I went wrong? So, I am supposed to find the points on the hyperboloid x^2-y^2+2z^2 = 1 where the normal line is parallel to the line that joins the points (3,-1,0) and (5,3,6).

    2. Relevant equations
    I think I'm supposed to find the gradient vector of the hyperboloid, because that has the direction of the normal line.

    3. The attempt at a solution
    So, if I'm right, the gradient of the hyperboloid is <2x, -2y, 2z>, and that is supposed to have the same direction as the vector <2, 4, 6>. So, wouldn't I just be looking for values of x, y, and z that is in multiples of <2, 4, 6>? That seems wrong to me. Thanks!!!
  2. jcsd
  3. Jan 28, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Wouldn't the gradient be <2x, -2y, 4z>? Then you'd need to find (x,y,z) such that <2x, -2y, 4z> is a scalar multiple of <2, 4, 6> AND (x,y,z) must lie on the given hyperboloid, i.e. it must satisfy x2 - y2 + 2z2 = 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook