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Let veca , vecb , vecc represent respec...

Let ` veca , vecb , vecc` represent respectively `vec(BC), vec(CA) and vec(AB) ` where ABC is a triangle , Then ,

A

`veca + vecb = vecc`

B

` vecb + vecc = veca`

C

` veca xx vecb = vecb xx vecc = vecc xx veca`

D

` [ veca vecb vecc] = [ vecb vecc veca] = [ vecc veca vecb] ne 0`

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
` vec(BC) + vec(CA) = vec(BA) `
` Rightarrow veca + vecb = -vecc`
` Rightarrow veca + vecb + vecc = vec0`
` Rightarrow veca xx ( veca + vecb + vecc) -veca xx vec0`
` Rightarrow veca xx vecb + veca xx vecc = vec0 Rightarrow veca xx vecb = vecc xx veca`
Similarly , we have, ` vecb xx vecc - vecc xx veca`
` veca xx vecb = vecb xx vecc = vecc xx veca `
Clearly, ` veca , vecb, vecc` are coplanar vectors.
` [ veca vecb vecc] = [ vecb vecc veca] = [ vecc veca vecb ] = 0`
So, option (d) is not correct. \
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