Question

: if (vector)a X (vector)b = (vector)c X (vector)b , is it possible to prove that (vector)a = (vector)c

Answer 1

is cross product commutable?

Answer 2

AB not= BA

Answer 3

But, its prolly not pertinent is it

Answer 4

there are more comprehensive proofs online then I can think up at the moment

Answer 5

why is cross product's commutability entering the matter ...it's already been stated the AB=CB

Answer 6

becasue that is what i thought about when I read your post, but after posting it i realized that it had nothing to do with the matter.

Answer 7

okay

Answer 8

Suppose a and c are not the same; and try to prove otherwise.


<a,b>x<m,n> = <c,d>x<m,n>

that might be something worth doing

Answer 9

no...
we cant say that because if (vector)a X (vector)b = (vector)c X (vector)b, it implies that absin(angle bet a &b)= bcsin(angle bet b &c), so even though it is stated in that way, u cant say vector a= vector c unless angles between a&b and b&c are equal...

I think this gives u ur required answer..

Answer 10

\[<a_1,a_2>x<b_1,b_2>=<c_1,c_2>x<b_1,b_2>\]
\[a_2b_1 -a_1b_2=c_2b_1-c_1b_2\]
\[a_2b_1-c_2b_1= a_1b_2-c_1b_2\]
\[b_1(a_2-c_2)= b_2(a_1-c_1)\]
anushas looks viable :)

Answer 11

thanks for the medals @amistre64 & siddarth95...

Answer 12

@anusha : .... thanks ...i think i understand it now :)

Answer 13

:)