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If veca, vecb and vecc are three non-cop...

If `veca, vecb and vecc` are three non-coplanar vectors, then find the value of `(veca.(vecbxxvecc))/(vecb.(veccxxveca))+(vecb.(veccxxveca))/(vecc.(vecaxxvecb))+(vecc.(vecbxxveca))/(veca.(vecbxxvecc))`

Text Solution

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Since ` (veca vecb vecc] ne 0`, we have
`(veca.(vecbxxvecc))/(vecb.(veccxxveca))+(vecb.(veccxxveca))/(vecc.(vecaxxvecb))+(vecc.(vecbxxveca))/(veca.(vecbxxvecc))=([veca vecb vecc])/([vecb vecc veca])+([vecbveccveca])/([vecc veca vecb])+([vecc vecb veca])/([veca vecb vecc])`
`= ([vecavecb vecc])/([veca vecbvecc])+([vecavecbvecc])/([vecavecbvecc])-([vecavecbvecc])/([veca vecb vecc])`
= 1+ 1 -1=1
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