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!

Identify these surfaces- quick vector question

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data
    Identify the following surfaces:
    i) r.u=L
    ii) r.u=mlrl for -1[itex]\leq[/itex]m[itex]\leq[/itex]1
    where k, L, m are fixed scalars and u is a fixed unit vector.

    2. Relevant equations

    3. The attempt at a solution
    The first one is in the same form as the equation of a plane, but u is not necessarily the normal, so I'm confused. For the second one, I have no idea.
  2. jcsd
  3. Oct 29, 2011 #2
    Is part i just an ordinary plane?
  4. Oct 29, 2011 #3

    I like Serena

    User Avatar
    Homework Helper

    Hi Lucy Yeats! :smile:


    r.u is the distance of point r to the surface perpendicular to u through the origin.

    With r.u=L you get all points with distance L to this surface, which is again a surface.
  5. Oct 29, 2011 #4

    I like Serena

    User Avatar
    Homework Helper

    As for part ii, you would get all points with distance m|r| to the plane normal to u and through the origin.

    Let's start with m=0. What is it?
    Now m=1: can you say in words which points you get?
  6. Oct 29, 2011 #5
    Since m is a fixed scalar, I don't think it changes. However, the modulus of r is increasing with distance from the origin. So do you get a kind of 3d parabola/ bowl shaped surface??
  7. Oct 29, 2011 #6

    I like Serena

    User Avatar
    Homework Helper

    Ah, you're ahead of me (but no, it is not a bowl :wink:).

    With m=0, you'd get r.u=0 which is a plane through the origin.

    With m=1, you'd get all points r with a distance to the plane that is equal to the distance of r to the origin.
    Which points would that be?
  8. Oct 29, 2011 #7
    All the points halfway between the origin and the surface?
  9. Oct 29, 2011 #8

    I like Serena

    User Avatar
    Homework Helper

    No. The surface we're talking about contains the origin.
    So there's no such thing as halfway.

    Perhaps you can make a drawing in 2 dimensions.
    Instead of a plane we'll have a line, but the principle remains the same.
    Let u=(0,1).
    What is the "plane" in this example?
    Can you find a point that has an equal distance to the origin as to the line representing the "plane"?
  10. Oct 29, 2011 #9


    User Avatar
    Homework Helper
    Gold Member

    How do you get r˙uusing the length of the vectors and the angle they enclose? Try to use this formula.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Identify these surfaces- quick vector question
  1. Quick vectors question (Replies: 2)

  2. Quick Vector Question (Replies: 1)