If `veca , vecb and vecc ` are three vectors such that `vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb` then prove that `|veca|= |vecb|=|vecc|`

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|`