`veca , vecb and vecc` are three non-coplanar vectors and `vecr`. Is any arbitrary vector. Prove that `[vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr`.

`veca , vecb and vecc` are three non-coplanar vectors and `vecr`. Is a

1.	`veca , vecb and vecc` are three non-coplanar vectors and `vecr`. Is any arbitrary vector. Prove that `[vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr`.
Answer» `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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`veca , vecb and vecc` are three non-coplanar vectors and `vecr`. Is any arbitrary vector. Prove that `[vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr`.

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