Results 1 to 8 of 8

Math Help - Normal To Plane

  1. #1
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1

    Normal To Plane

    The plane P1 passes through the P, with position vector i + 2jk, and is perpendicular to the line L with equation

    r = 3i – 2k +l(-i + 2j + 3k)

    They got the normal to the plane to be : – i + 5j + 3k

    How did they get that? Thanks in advance.

    (Sorry for the strange font, I can't be bothered to edit the font.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Air View Post
    The plane P1 passes through the P, with position vector i + 2j k, and is perpendicular to the line L with equation


    r = 3i 2k +l(-i + 2j + 3k)



    They got the normal to the plane to be : i + 5j + 3k

    How did they get that? Thanks in advance.

    (Sorry for the strange font, I can't be bothered to edit the font.)
    Looks like they made a typo ....

    Since the line is perpendicular to the plane and a vector in the direction of the line is -i + 2j + 3k, a normal to the plane will be -i + 2j + 3k, NOT i + 5j + 3k ......
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1
    Quote Originally Posted by mr fantastic View Post
    Looks like they made a typo ....

    Since the line is perpendicular to the plane and a vector in the direction of the line is -i + 2j + 3k, a normal to the plane will be -i + 2j + 3k, NOT – i + 5j + 3k ......
    So a line in the form:

    r = a + \lambda b where 'a' is position vector and 'b' is direction vector. If this is perpendicular to a plane, does that always mean that the 'n' for the plane is 'b'.

    So r.n=a.n < Equation of plane. n is normal which the direction vector of a perpendicular line.

    Is that correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591
    Quote Originally Posted by Air View Post
    So a line in the form:

    r = a + \lambda b where 'a' is position vector and 'b' is direction vector. If this is perpendicular to a plane, does that always mean that the 'n' for the plane is 'b'.

    So r.n=a.n < Equation of plane. n is normal which the direction vector of a perpendicular line.

    Is that correct?

    EDIT: It can't be a typo as they wanted us to show that the cartesian equation of the plane is x-5y-3z=6 which wouldn't work if we used -i+2j+3k.
    May as well post the entire question, I agree with Mr F. Looks like they typoed in the question.
    Attached Thumbnails Attached Thumbnails Normal To Plane-picture-8.png  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Air View Post
    So a line in the form:

    r = a + \lambda b where 'a' is position vector and 'b' is direction vector. If this is perpendicular to a plane, does that always mean that the 'n' for the plane is 'b'. Mr F says: Yes.

    [snip]

    EDIT: It can't be a typo as they wanted us to show that the cartesian equation of the plane is x-5y-3z=6 which wouldn't work if we used -i+2j+3k.
    They are wrong. I'd say the typo is in the given equation of the line .... it should be r = 3i - 2k + \alpha (-i + 5j + 3k) ......
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1
    Another Question:
    The Points A, B and C lie on the plane P and, relative to a fixed origin O, they have position vectors
    a = 3i - j + 4k, b = -i + 2j, c = 5i - 3j + 7k

    Find an equation of Pin the form r.n = p.



    ^ I worked out direction vector of AB and AC but how do I work out n?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591
    Quote Originally Posted by Air View Post
    Another Question:
    The Points A, B and C lie on the plane P and, relative to a fixed origin O, they have position vectors
    a = 3i - j + 4k, b = -i + 2j, c = 5i - 3j + 7k

    Find an equation of Pin the form r.n = p.



    ^ I worked out direction vector of AB and AC but how do I work out n?
     \overrightarrow{AC} \times \overrightarrow{AB}

    Bobak
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Air View Post
    Another Question:
    The Points A, B and C lie on the plane P and, relative to a fixed origin O, they have position vectors

    a = 3i - j + 4k, b = -i + 2j, c = 5i - 3j + 7k


    Find an equation of Pin the form r.n = p.



    ^ I worked out direction vector of AB and AC but how do I work out n?
    n will be the cross (vector) product of AB and AC:

    n = AB x AC.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intersection of a plane and a normal.
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: June 4th 2011, 06:49 PM
  2. Normal equation of a plane
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 31st 2011, 12:53 AM
  3. Normal Plane help
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 5th 2010, 01:20 PM
  4. Normal to Plane
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 10th 2010, 05:50 PM
  5. normal plane to the curve intersecting a plane
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 23rd 2009, 09:53 AM

Search Tags


/mathhelpforum @mathhelpforum