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
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.
"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.
I told you that this is a nightmare of subscripts. Using my suggested notation.
$\displaystyle \begin{align*}(A\cdot C)B &=(a_xc_x+ a_yc_y+ a_zc_z)(b_xi+b_yj+b_zk)\\ &=(a_xb_xc_x+ a_yb_xc_y+ a_zb_xc_z)i \\&~+(a_xb_yc_x+ a_yb_yc_y+ a_zb_yc_z)j\\&~+(a_xb_zc_x+ a_yb_zc_y+ a_zb_zc_z)k \end{align*}$.