Results 1 to 2 of 2

Math Help - (a*b) * (c *d) =0

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    123

    Question (a*b) * (c *d) =0

    Could you please teach me how to solve this question? I don't know how to do it at all. Thank you very much.

    Question:
    Prove: If a , b, c, and d lie in the same plane when positioned with a common initial point then (a*b) * (c *d) =0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Jenny20 View Post
    Could you please teach me how to solve this question? I don't know how to do it at all. Thank you very much.

    Question:
    Prove: If a , b, c, and d lie in the same plane when positioned with a common initial point then (a*b) * (c *d) =0.
    \bold{a} \wedge \bold{b} is a vector normal to the plane containg \bold{a} and \bold{b}. Similarly \bold{c} \wedge \bold{d} is a vector normal to the plane containg \bold{c} and \bold{d}.

    But these two planes are the same plane so \bold{a} \wedge \bold{b} and \bold{c} \wedge \bold{d} are parallel (or anti-parallel) and hence:

    (\bold{a} \wedge \bold{b}) \wedge (\bold{c} \wedge \bold{d})=0

    RonL
    Last edited by CaptainBlack; January 2nd 2007 at 02:31 PM.
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum