If the points `P( veca + 2 vec b + vec c ), Q (2 veca + 3 vecb), R (vecb+ t vec c ) ` are collinear, where `veca , vec b , vec c ` are non-coplanar vectors, the value of t is

If the points P(vec a + 2 vec b + vec c), Q (2 vec a + 3 vec b), R(vec b + t vec c) are collinear, where vec a, vec b, vec c are three non-coplanar vectors, the value of t is

If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd , where veca, vecb are non-collinear and vec c, vec d are also non-collinear then :

If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd , where veca, vecb are non-collinear and vec c, vec d are also non-collinear then :

Let vecr=sinx (veca xx vecb)+cosy(vecb xx vec c)+2(vec c xx veca) , where veca, vecb are non-collinear and vec c, vecd are also non-collinear then :

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

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) .

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

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