If `veca, vecb, vecc` are three vectors, then
`[(vecaxxvecb, vecbxxvecc, veccxxveca)]=`

Options

A. `[(veca, vecb, vecc)]`
B. `2[(veca, vecb, vecc)]`
C. `3[(veca, vecb, vecc)]`
D. `[(veca, vecb, vecc)]^(2)`

Answer

D

Explanation

We have
`[(vecaxxvecb, vecbxxvecc, veccxxveca)]`
`={(vecaxxvecb)xx(vecbxxvecc)}.(veccxxveca)`
`={vecd xx (vecbxxvecc)}.(veccxxveca)`, where `vecd=vecaxxvecb`
`={(vecd.vecc)vecb-(vecd.vecb}.(veccxxveca)`
`={((vecaxxvecb).vecc)vecb-((vecaxxvecb).vecb)vecc}.(veccxxveca)`
`implies{[(veca, vecb, vecc)]vecb-[(veca, vecb, vecb)]vecc}.(veccxxveca)`
`={[(veca vecb, vecc)]vecb-(0)vecc}.(vecxxveca)[ :' [(veca, vecb, vecb)]=0]`
`={[(veca, vecb, vecc)]vecb}.(veccxxveca)`
`=[(veca, vecb, vecc)]{vecb.(veccxxveca)}`
`[(veca, vecb, vecc)], [(vecb, vecc, veca)=[(veca, vecb, vecc)]^(2)`
`[ :' [(veca, vecb, vecc)]=[(vecb, vecc, veca)]]`