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Let veca, vecb and vecc be three non- co...

Let `veca, vecb and vecc` be three non- coplanar vectors and `vecr` be any arbitrary vector. Then `(vecaxxvecb) xx (vecr xxvecc) + (vecbxxvecc)xx(vecrxxveca)+ (vecc xxveca) (vecrxxvecb)` is always equal to

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`Let" " vecr=x_(1)veca+x_(2)vecb+x_(3)veccRightarrow vecr.(vecbxxvecc)=x_(1)veca.(vecbxxvecc)or x_(1)=([vecr vecb vecc])/([veca vecb vecc])`.
`Also, " " vecr.(veccxxveca)=x_(2)vecb.(veccxxveca)orx_(2)=([vecrveccveca])/([vecavecbvecc])`
`and vecr.(vecaxxvecb)=x_(3)vecc. (vecaxxvecb)or x_(3)=([vecr vecavecb])/([veca vecbvecc])`
`Rightarrow vecr=([vecrvecb vecc])/([vecavecbvecc])veca+([vecrveccveca])/([vecavecbvecc])vecb+([vecrvecavecb])/([vecavecb vecc])vecc`
`or [vecbveccvecr]veca+[veccvecavecr]vecb+[vecavecbvecr]vecr=[vecavecbvecc]vecr`
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