Results 1 to 2 of 2

Math Help - Lines Planes and vectors in R3 Problem

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    1

    Lines Planes and vectors in R3 Problem

    If the line is parallel to the vector v = < -2,1,3>, what is the equation of the plane containing L and the point B = (-2,3,1)

    A) - x + y + z = 6
    B) 3x - 2y - z = 4
    C) x + 6y -11z = 5
    D) x + 5y - z = 12
    E) 2x + 10y - 19z = 7

    I know we can get the equation of the line because we have a point on the line and a vector parallel

    So x = xo + at, y = yo + bt , z = zo + ct

    x = -2 + -2t
    y = 3 + t
    z = 1 + 3t

    I know the equation of a plane is a(x - xo) + b(y - yo) + c(z - zo) = 0. But the vector here <a,b,c> has to be normal to the plane...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,234
    Thanks
    1795
    Are we to assume that "L" is the line parallel to the given vector?

    If so, you are misinterpreting the problem. The point (-2, 3, 1) cannot be on the line. If it were, there would be an infinite number of planes passing through that line (and point). L must be any other line, parallel to that vector, not containing that point.

    Write x= x_0- 2t, y= y_0+ t, z= z_0+ 3t where you are free to choose (x_0, y_0, z_0) as long as it gives a line not passing through (-2, 3, 1). For example, taking x_0= y_0= z_0= 0 gives x= -2t, y= t, z= 3t which does NOT pass through (-2, 3, 1) because if y= t= 3 then z= 3t= 9\ne 1.

    You can find another vector in the plane by taking a vector from any given point on that line to (-2, 3, 1). For example, taking t= 0 gives (0, 0, 0) so another vector in the plane is <-2, 3, 1>. The cross product of that and the given vector is normal to the plane.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 18th 2010, 12:52 AM
  2. Vectors - Lines and Planes Question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 16th 2010, 07:07 PM
  3. Help with Lines/Planes/Vectors
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 13th 2009, 02:51 PM
  4. Vectors, lines, and planes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 20th 2008, 12:10 PM
  5. vectors.lines.planes
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 2nd 2007, 08:46 PM

Search Tags


/mathhelpforum @mathhelpforum