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  4. If a.b=b.c=c.a=0, then a.(b× c) is equal to

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Q. If $ a.b=b.c=c.a=0, $ then $ a.(b\times c) $ is equal to

Rajasthan PETRajasthan PET 2011

Solution:

$ a.(b\times c)=|a|b\times c|\cos \theta ,\theta =0 $ or $ \pi $ ( $ \because $ $ a.b=b.c=c.a=0, $ therefore, a,b,c are mutually at right angles and hence $ b\times c $ is parallel to a)
$ \therefore $ $ a.(b\times c)=|a|(|b||c|\sin 90{}^\circ ) $ $ =|a||b||c| $