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

Monotone Test of the equation

  1. May 15, 2009 #1
    Hi all:

    Assume in 3D space there is a point [itex]v=[v_x, v_y, v_z][/tex], and a normal vector associate with it as [tex]n=[n_x, n_y, n_z][/tex]. A line function is defined as [tex]u=w+t\cdot l[/tex] where [tex]w=[w_x, w_y, w_z][/tex] is a point, and [tex]l=[l_x, l_y, l_z][/tex] is the normalized direction of the line. l and n are normalized. Assume there is a function defined as:

    K = \frac{(u-v)\cdot n}{||u-v||^2}

    My question is when point u varies on the line, is the function K varies monotonically???

    I've tried to compute [tex]\frac{dK}{dt}[/tex], but I can't really see if it's monotone or not, can some one help me please?

    Last edited: May 15, 2009
  2. jcsd
  3. May 15, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi Asuralm! :smile:

    Forget calculus, this is geometry :wink:

    Hunt: if u and v represent points U and V, and if the nearest point on L to U is N, what is (u - v).n ? :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook