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

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)/([barabarbbarc]),barb^(1)=(barcxxbara)/([barabarbbarc]) and barc^(1)=(baraxxbarb)/([barabarbbarc]) then prove that [barabarbbarc][bara^(1)barb^(1)barc^(1)]=1

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

bara.barb^(1)+barb.barc^(1)+barc.bara^(1)=

bara,barb,barc are non-coplanar and barl=(barbxxbarc)/([bara barb barc]),barm=(barcxxbara)/([bara barb barc]),barn=(baraxxbarb)/([bara barb barc]) then (bara+barb+barc).(barl+barm+barn)=

If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([bara barb barc]),barq=(barcxxbara)/([bara barb barc]),barr=(baraxxbarb)/([bara barb barc]) then (bara+barb).barp+(barb+barc).barq+(barc+bara).barr =

If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([barabarbbarc]),barq=(barcxxbara)/([barabarbbarc]),barr=(baraxxbarb)/([barabarbbarc]) then (2bara+3barb+4barc).barp+(2barb+3barc+4bara).barq+(2barc+3bara+4barb).barr =

If bara,barb,barc are non-coplanar vectors and (bara+2barb+barc).(bara-barb)xx(bara-barb-barc)=lamda[barabarbbarc] then lamda =

Let bara,barb and barc be non coplanar vectors if [2bara-barb+3barc,bara+barb-2barc,bara+barb-3barc]=lamda[bara barb barc] then find lamda .