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For any four vectors prove that (vecbx...

For any four vectors prove that
`(vecbxxvecc).(veca xxvecd)+(vecc xxveca).(vecbxxvecd)+(vecaxxvecb).(veccxxvecd)=0`

Text Solution

Verified by Experts

`(vecbxxvecc).(vecaxxvecd)=(vecb.veca)(vecc.vecd)-(vecb.vecd)(vecc.veca)`
`(veccxxveca).(vecbxxvecd)=(vecc.vecd)(veca.vecd)-(vecc.vecd)(veca.vecb)`
`(vecaxxvecb).(veccxxvecd)+(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc)`
`Rightarrow (vecbxxvecc).(vecaxxvecd)+(veccxxveca).(vecbxxvecd)+(vecaxxvecb).(vecc xxvec)=0`
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