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If the vectors a, b and c are coplanar, then |(a,b,c),(a.a,a.b,a.c),(b.a,b.b,b.c)| is equal to

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None of these

Solution :Since a, b and c are COPLANAR, there must EXIST three scalars x,y and z not all zero such that
`ax+yb+zc=0""…(i)`
ON multiplyaing both sids of Eq (i) by a and b respectively we get
`xaa+ya.b+za.c =0:""…(II)`
`ab.a+yb.b+zb.c=0""...(iii)`
On eliminating x,y and z from Eqs, (i), (ii) and (iii), we get
`|{:(a,b,c),(a.a., a.b.,b.c),(b.a, a.b, b.c):}|=0`


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