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if veca , vecb ,vecc are three vectors...

if ` veca , vecb ,vecc ` are three vectors such that ` veca +vecb + vecc = vec0` then

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
we have,
` veca +vecb +vecc= vec0`
` Rightarrow veca xx (veca + vecb + vecc ) = veca xx vec0` [ Taking cross product with `veca` ]
` Rightarrow veca +veca + veca xx vecb + vecc xx veca =0`
` Rightarrow vec0 + veca xx vecb -vecc xx veca =0`
` Rightarrow veca xx vecb = vecc xx veca`
Taking cross product of (i) with ` vecb, " we get " veca xx vecb = vecb xx vecc`
` veca xx vecb = vecc xx veca`
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