Results 1 to 7 of 7

Math Help - Planes in space

  1. #1
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19

    Planes in space

    I need to find the plane A that contains the line r_A(t)=<3+2t , t , 8-t> and is parallel to the plane B, 2x+4y+8z=17

    I know that the normal vectors n_A=<a,b,c>,n_B=<2,4,8> should have a dot product equal to one. also know that the points (3,1,7),(7,2,6) lie on the line r_A(t), correpsonding to t=1,t=2. The points are also the terminal points of the vectors <3,1,7>,<7,2,6>. Substracting these vectors, I write the vector equation of the plane A as

    (1) n_A\cdot<4,1,-1>=0.

    The problem is that I don't know how to find the vector n_A. I know that n_A,n_B are parallel so

    (2) n_A\cdot n_B=\mid n_A n_B\mid\cos\theta_{A,B}

    I can only solve this for the magnitude of n_A. How do I get the vector? Secondly, I need to know if I'm setting this up right. Is equation (1) correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    All you need for the equation of a plane is a point in the plane and vector normal to it.

    They give you the normal vector by saying that there is a parallel plane with the corresponding normal vector: <2, 4, 8>

    So all you need now is a point within the plane and you can use the equation:
    v_1(x - x_1) + v_2(y - y_1) + v_3(z - z_1) = 0

    Where (x_1, y_1, z_1) are the coordinates of a point you need to find, and <v_1, v_2, v_3> = <2, 4, 8>
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,675
    Thanks
    1618
    Awards
    1
    Quote Originally Posted by adkinsjr View Post
    I need to find the plane A that contains the line r_A(t)=<3+2t , t , 8-t> and is parallel to the plane B, 2x+4y+8z=17
    I know that the normal vectors n_A=<a,b,c>,n_B=<2,4,8> should have a dot product equal to one. also know that the points (3,1,7),(7,2,6) lie on the line r_A(t), correpsonding to t=1,t=2. The points are also the terminal points of the vectors <3,1,7>,<7,2,6>. Substracting these vectors, I write the vector equation of the plane A as
    First of all (3,1,7) is not on the line.
    When t=0 the point (3,0,8) is on the line.

    Any plane parallel to 2x+4y+8z=7 looks 2x+4y+8z=K.
    Use the point (3,0,8) to find the value of K.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Quote Originally Posted by Plato View Post
    First of all (3,1,7) is not on the line.
    When t=0 the point (3,0,8) is on the line.

    Any plane parallel to 2x+4y+8z=7 looks 2x+4y+8z=K.
    Use the point (3,0,8) to find the value of K.
    Ok, so basically when ever I have two planes that are parallel, I can immediately assume that they have the same normal vector?

    n_A=<2,4,8>

    I should be able to write the equation of the plane as:

    n_A\cdot <r-r_o(0)>=0

    <2,4,8>\cdot (<x,y,z> - <3,0,8>)=0
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,675
    Thanks
    1618
    Awards
    1
    Quote Originally Posted by adkinsjr View Post
    Ok, so basically when ever I have two planes that are parallel, I can immediately assume that they have the same normal vector?

    n_A=<2,4,8>

    I should be able to write the equation of the plane as:

    n_A\cdot <r-r_o(0)>=0

    <2,4,8>\cdot (<x,y,z> - <3,0,8>)\color{red}=0
    See the correction above. That gives the correct answer.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    Quote Originally Posted by adkinsjr View Post
    Ok, so basically when ever I have two planes that are parallel, I can immediately assume that they have the same normal vector?

    n_A=<2,4,8>

    I should be able to write the equation of the plane as:

    n_A\cdot <r-r_o(0)>=0

    <2,4,8>\cdot (<x,y,z> - <3,0,8>)=0

    Bingo.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Cool, thanks for your help folks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. planes in space
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 26th 2010, 11:36 AM
  2. Equatisonf of Planes in 3-space
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 11th 2009, 05:39 PM
  3. Planes in space (again)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 9th 2009, 11:48 AM
  4. Planes in 3-space; Equations of planes
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: July 30th 2008, 03:01 PM
  5. planes in 3-space
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 12th 2006, 06:13 PM

Search Tags


/mathhelpforum @mathhelpforum