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Math Help - its a prove question ax(bxc)=....

  1. #1
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    its a prove question ax(bxc)=....

    the question is a X (b X c)= (A.C)B - (A.B)C

    THE DOT MEANS THOSE BIG DOTS BTW,
    im not sure if you need what a b and c are but here they are,

    a=9i-9j-4k
    b=i-4j-2k
    c=7i+j+9k
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  2. #2
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    Re: its a prove question ax(bxc)=....

    Quote Originally Posted by newkidz View Post
    the question is a X (b X c)= (A.C)B - (A.B)C

    If you are asked to prove, it is a messy, messy exercise in subscripts.

    Let A=<a_x,a_y,a_z>.~B=<b_x,b_y,b_z>.~C=<c_x,c_y,c_z>.  ~

    Now do the cross-products , rearrange and factor to get (A\cdot C)B-(A\cdot B)C.
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    Re: its a prove question ax(bxc)=....

    how do i cross product it 3 times,
    i did b X c, and got i[ByCz-BzCy]-j[BxCz-BzCx]+k[BxCy-ByCx]
    am i ment to cross product that against A=ax,ay,az.

    also when i did it with my numbers i got -169i-125j-99k for Ax(Bxc)
    but when you do (A.c) i get a single digit of 18 so not sure what to do

    and lastly for the RHS there is no dot or multiply what does that mean, (a.c)b.
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    Re: its a prove question ax(bxc)=....

    "A single digit of 18"? That's two digits! You mean a single NUMBER.

    The cross product of two vectors is a vector and when you take the cross product of that with another vector, you get a vector again. That is, the left side of the equation is a vector and so the right side must also be a vector. Yes, the dot product of two vectors is a number and then (A.C)B means that you multiply that number by the vector B just as, for example, "2B". A number times a vector is a vector.
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    Re: its a prove question ax(bxc)=....

    Quote Originally Posted by newkidz View Post
    how do i cross product it 3 times,
    i did b X c, and got i[ByCz-BzCy]-j[BxCz-BzCx]+k[BxCy-ByCx]
    am i ment to cross product that against A=ax,ay,az.

    I told you that this is a nightmare of subscripts. Using my suggested notation.

    \begin{align*}(A\cdot C)B &=(a_xc_x+ a_yc_y+ a_zc_z)(b_xi+b_yj+b_zk)\\ &=(a_xb_xc_x+ a_yb_xc_y+ a_zb_xc_z)i \\&~+(a_xb_yc_x+ a_yb_yc_y+ a_zb_yc_z)j\\&~+(a_xb_zc_x+ a_yb_zc_y+ a_zb_zc_z)k \end{align*}.
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    Re: its a prove question ax(bxc)=....

    Please leave it here. newkidz has been posting graded questions.

    -Dan
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