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![[Post New]](/templates/default/images/icon_minipost_new.gif) 29 Jan 2008 23:20:11 IST
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1)
as a,b,c lie in same plane so
a*b is perp. to the plane ABC
b*c is perp. to the plane ABC,
similarly for c*a...
as a*b, b*c, c*a all lie in plane perpendicular to tht of ABC,
so a*b +b*c+c*a lies in plane perpendicular to tht of ABC
aliter
let a*b+b*c+c*a lie in any plane perp to ABC
then its dot product with any of a,b,c shud be zero
on taking dot product with a
we get [aba] + [bca] + [caa]
[aba]=[caa]=0
and since b,c,a are coplanar so [abc] =0
thus dot product is zero so the vector lies in plane perp to ABC
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