If ` vec a , vec b`, and `vec c` are three vectors such that ` vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b ,` then prove that `| vec a|=| vec b|=| vec c|`.

Explanation

`here, vecaxxvecb=vecc`
`(vecaxx vecb) .vecc=vecc.vecc`
`[veca vecbvecc] =| vecc|^(2)`
`Also, vecbxxvecc=veca`
`Rightarrow (vecbxxvecc) .veca=veca.veca`
`Rightarrow [vecb veccveca] = |veca|^(2)`
also ,` vecc xxveca =vecb`
`(vecc xxveca).vecb=vecb.vecb`
`[vecc veca vecb] =|vecb|^(2)`
since, `[veca vecb vecc] = [vecb vecc veca] =[ vecc veca vecb],`
`|veca|=|vecb|=|vecc|`