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If veca,vecb and vecc are three non copl...

If `veca,vecb and vecc` are three non coplanar vectors and `vecr` is any vector in space, then `(vecaxxvecb)xx(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)=`

A

`2[(veca, vecb, vecc)]vecr`

B

`3[(veca, vecb, vecc)]vecr`

C

`[(veca, vecb, vecc)]vecr`

D

none of these

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The correct Answer is:
A
We have
`(vecaxxvecb)xx(vecrxxvecc)=[(veca, vecb, vecc)]vecr-[(veca, vecb, vecr)]vecc`
`(vecbxxvecc)xx(vecrxxveca)=[(vecab, vecc, veca)]vecc-[(vecb, vecc, vecr)]veca`
`(veccxxveca)xx(vecrxxvecc)=[(vecc, veca, vecb)]vecr-[(vecc, veca, vecr)]vecb`
`:.(vecaxxvecb)xx(vecrxxvecc)+(vecbxxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)`
`=3[(veca, vecb, vecc)]vecr-[(veca, vecb, vecc)]vecc+[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb`
`=3[(veca, vecb, vecc)]vecr=[(veca, vecb, vecc)]vecr=2[(veca, vecb, vecc)]vecr`.
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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
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