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If the vectors vec a , vec b ,a n d vec...

If the vectors ` vec a , vec b ,a n d vec c` form the sides`B C ,C Aa n dA B ,` respectively, of triangle `A B C ,t h e n`

A

`veca.vecb+ vecb.vecc+vecc.veca=0`

B

`vecaxxvecb = vecbxxvecc =veccxxveca`

C

`veca.vecb = vecb.vecc = vecc.veca`

D

`vecaxxvecb + vecbxxvecc +veccxxveca=vec0`

Text Solution

Verified by Experts

The correct Answer is:
b
Given `veca +vecb +vecc= vec0` (by triangle law). Therefore,
`veca xx (veca +vecb+vecc)=veca xxvec0`
`veca xx veca +veca xx vecb+ veca xx vecc=vec0`
`veca xx vecb = vecc xx veca`
Similarly by taking cross product with `vecb`. We get `veca xx vecb = vecb xx vecc`
`veca xx vecb = vecb xx vecc= vecc xx veca`
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