Prove that `[veca + vecb, vecb + vec, c vec c+veca]=2[veca vec b vec c].`

If [veca+vecb, vecb+vec c, vec c+veca]=8 then [veca, vecb, vec c] is

If [veca xx vecb vecb xx vec c vec c xx vec a] = lamda [veca vecb vec c ]^2 then lamda is equal to

Let veca , vecb, vec c be three non coplanar vectors , and let vecp , vecq " and " vec r be the vectors defined by the relation vecp = (vecb xx vec c )/([veca vecb vec c ]), vec q = (vec c xx vec a)/([veca vecb vec c ]) " and " vec r = (vec a xx vec b)/([veca vecb vec c ]) Then the value of the expension (vec a + vec b) .vec p + (vecb + vec c) .q + (vec c + vec a) . vec r is equal to

Prove that : veca*(vecb+vec c)xx(veca+2vecb+3vec c)=[veca vecb vec c]

Prove that veca*(vecb+vec c)xx (veca+3vecb+2vec c)=-(veca vecb vecc )

If [vec a vecb vec c] ne 0 and vecP=(vec b xx vec c)/([veca vecb vec c]), vecq=(vec c xx veca)/([veca vec b vec c]), vec r =(vec a xx vec b)/([veca vecb vec c ]) , then veca. vecp+ vecb. vecq+ vec c.vecr is equal to …………

Show that [vecb, vec c, vecd]veca-[veca, vec c, vecd]vecb+[veca, vecb, vecd]vec c-[veca, vecb, vec c]vecd=0 .

It is given that : vec x = (vec b xx vec c)/([veca vec b vec c]) ; vecy=(vec c vec a)/([veca vecb vecc]) ; vecz=(veca xx vecb)/([veca vecb vecc]) where a, b, c are non-coplanar vectors; show that x, y, z also form a non-coplanar system. Find the value of vecx*(veca+vecb)+vecy*(vecb+vecc)+vecz(vecc+veca) .

i. If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3veca -7vecb -4 vecc ,3 veca -2vecb + vecc and veca + vecb +2 vecc are coplanar.

If vec a , vec b and vec c are such that veca xx vecb = vecc and vecb xx vec c = vec a , prove that veca , vecb and vecc are mutually perpendicular |vecb| =1 and |vecc| = |veca| .