If `bara,barb,barc` are three non coplanar vectors `barp=((barbxxbarc))/([bara barb bar c]),bar q=(barcxxbara)/([bara barb barc]),barr=(baraxxbarb)/([bara bar b barc])` then `(2bara+3barb+4barc)*barp+(2barb+3barc+4bara)*barq+(2barc+3bara+4barb)*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 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 non-coplaner vectors and barp=(barbxxbarc)/([barabarb barc]),barq=(barcxxbara)/([barabarb barc]),barr=(baraxxbarb)/([barabarb barc]) then bara.barp+barb.barq+barc.barr=

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 non-coplaner vectors and barp=(barbxxbarc)/([barb barcbara]),barq=(barcxxbara)/([barcbarabarb]),barr=(baraxxbarb)/([barabarb barc]), then : (barb+barc).barp+(barc+bara).barq+(bara+barb).barr=

If bara,barb,barc are three non-coplanar vectors and barp,barq,barr are defined by the relations 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 and barp,barq,barr are defined by the relations 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=

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