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Show that bara.[(barb+barc)xx(bara+bar...

Show that
`bara.[(barb+barc)xx(bara+barb+barc)]=0`

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barc.(barb+barc)xx(bara+barb+barc)=

Show that (bara+barb).(barb+barc)xx(barc+bara)=2[barabarbbarc]

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If [bara barb barc ] = 1 then show that (bara.bara)(barbxxbarc)+ (bara.barb)(barcxxbara)+(bara.barc)(baraxxbarb)=bara .

Show that (baraxx(barbxxbarc))xxbarc=(bara.barc)(barbxxbarc) and ((baraxxbarb).(baraxxbarc)+bara.barb)(bara.barc)=(bara.bara)(barb.barc)

If bara,barb,barc are any three vectors such that (bara+ barb) . barc = (bara - barb) . barc = 0 then (baraxx barb)xxbarc =

[bara barb barc]+[bara barc barb] =

Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([bara barb barc]),barb^(1)=(barcxxbara)/([bara barb barc]) and barc^(1)=(baraxxbarb)/([bara barb barc]) then prove that (bara+barb+barc).(bara^(1)+barb^(1)+barc^(1))=3

Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([bara barb barc]),barb^(1)=(barcxxbara)/([bara barb barc]) and barc^(1)=(baraxxbarb)/([bara barb barc]) then prove that bara.bara^(1)=barb.barb^(1)=barc.barc^(1)=1

Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([bara barb barc]),barb^(1)=(barcxxbara)/([bara barb barc]) and barc^(1)=(baraxxbarb)/([bara barb barc]) then prove that bara.barb^(1)=bara.barc^(1)=barb.bara^(1)=barb.barc^(1)=barc.bara^(1)=barc.barb^(1)=0