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  4. If the three vectors A,B and C satisfy the relation A.B=0 and A.C=0, then vector A is parallel to

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Q. If the three vectors A,B and C satisfy the relation $ A.B=0 $ and $ A.C=0, $ then vector A is parallel to

Jharkhand CECEJharkhand CECE 2013

Solution:

Given. $ A.B=0,\, $
$ \therefore $ A is $ \bot $ to B also $ A.C=0, $
$ \therefore $ A is $ \bot $ to C
As $ B\times C $ is $ \bot $ to both B and C,
so $ B\times C $ is parallel to A.