Results 1 to 3 of 3

Math Help - Vector proof

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    159

    Vector proof

    Show that vectors (b dot c)a - (a dot c)b and vector c are perpendicular. Any advice is appreciated. Frostking
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Frostking View Post
    Show that vectors (b dot c)a - (a dot c)b and vector c are perpendicular. Any advice is appreciated. Frostking
    Let \mathbf{z}=\left(\mathbf{b}\cdot\mathbf{c}\right)\  mathbf{a}-\left(\mathbf{a}\cdot\mathbf{c}\right)\mathbf{b}

    Thus, you want to show that \mathbf{z}\cdot\mathbf{c}=0

    I'll start you off and then I'll let you finish

    \mathbf{z}\cdot\mathbf{c}=\left[\left(\mathbf{b}\cdot\mathbf{c}\right)\mathbf{a}\r  ight]\cdot\mathbf{c}-\left[\left(\mathbf{a}\cdot\mathbf{c}\right)\mathbf{b}\r  ight]\cdot\mathbf{c}=\left(\mathbf{b}\cdot\mathbf{c}\ri  ght)\left(\mathbf{a}\cdot\mathbf{c}\right)-\left(\mathbf{a}\cdot\mathbf{c}\right)\left(\mathb  f{b}\cdot\mathbf{c}\right)=\dots

    Does this make sense?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    It helps to know that C \times \left( {A \times B} \right) = \left( {C \cdot B} \right)A - \left( {C \cdot A} \right)B
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector Proof Help
    Posted in the Geometry Forum
    Replies: 5
    Last Post: November 18th 2010, 06:45 PM
  2. Vector proof
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 13th 2010, 06:41 AM
  3. Vector Proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 7th 2009, 07:32 PM
  4. Vector Proof
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 19th 2008, 08:33 AM
  5. Vector Proof
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: February 28th 2008, 04:10 AM

Search Tags


/mathhelpforum @mathhelpforum