1. Not finding help here? Sign up for a free 30min 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!

Lines and Planes Confusion

  1. Apr 2, 2013 #1
    I having trouble understanding the difference between parallel and orthogonal in relation to finding the relevant line or plane equations.

    Example;

    Determine the vector and Cartesian line if:
    a) passes through (2,1,-3) and is parallel to v=(1,2,2)
    What would happen if it was perpendicular though?

    And the other one pertains to planes;
    Plane passes through point (1,4,5) and perpendicular to (7,1,4).

    I'm having confusion on what would happen if the opposites happened for both cases.
     
  2. jcsd
  3. Apr 2, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Then it would not be "well defined". In two dimensions, there would be exactly one line thorugh a given point perpendicular to a given line but in three dimensions, there are an infinite number of lines perpendicular to the given line- all lying in the plane perpendicular to the given line containing the given point.

    I assume you mean the vector (7, 1, 4). That's why I prefer to write vectors as <x, y, z> rather than (x, y, z)- to avoid confusing them with points. If (x, y, z) is a point in that plane then <x- 1, y- 4, z- 5> is a vector lying in the plane. It must be perpedicular to the vector <7, 1, 4> so the dot product <7, 1, 4>.<x-1, y- 4, z- 5>= 7(x- 1)+ 1(y- 4)+ 4(z- 5)= 0.

    What "opposite" do you mean for the second case?
    A line is one dimensional. In two- dimensions, there is only "other" coordinate so we can write y= ax+ b. In three dimensions there are two "other" coordinates so, to describe a line, we must use two equations, y= ax+ b, z= cx+ d, or use three "parametric equations".
     
  4. Apr 3, 2013 #3
    Is it right to assume that,
    To find vector equations for lines in r2 and r3, we'd generally use the equation,
    R=Ro+tV, where Ro represents a point the line pass and V presents the vector parallel to the line, what if that vector was perpendicular instead? That's what confuses me the most.

    And for plane equations I'm having trouble understanding the relationship of the normal vector to finding a planes equation, despite seeing proofs that relate them.
     
  5. Apr 3, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes.
    First, find a vector orthogonal to V. In 2D, swap the x and y values in V and negate one of them. In 3D, as Halls says, there are multiple solutions. there is an entire plane orthogonal to V and any vector in it would do.
    In 3D, there is a unique line through a point orthogonal to a given plane, and a unique plane through a point orthogonal to a given line. How would you represent a plane?
     
  6. Apr 3, 2013 #5
    I've just ot one more thing that's concerning me, for a question such as, find Cartesian and vector equations of a plane perpendicular to (1,0-2) and containing the point (1,-1,-3), my professor seemed to just use formula A(X-Xo)+B(Y-Yo)+C(Z-Zo)=o, and then just assigned parameters to determine the vector equation.

    Yet the textbook seems to use the idea that, X=Xo+sV+tU, where V and U are parallel to the plane and not each other...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Lines and Planes Confusion
  1. Lines and planes (Replies: 5)

Loading...