If `veca=mvecb+vecc`. The scalar m is

Prove that the necessary and sufficient condition for three vectors veca,vecb and vecc to be coplanar is that there exist scalars l,m,n (not all zero simultaneously) such that lveca+mvecb+nvecc=vec0 .

veca.(vecbxxvecc) is called the scalar triple product of veca,vecb,vecc and is denoted by [veca vecb vecc] . If veca,vecb,vecc are coplanar then [veca+vecb vecb+vecc vecc+veca ] = (A) 1 (B) -1 (C) 0 (D) none of these

If veca, vecb, vecc are non coplanar vectors and vecp, vecq, vecr are reciprocal vectors, then (lveca+mvecb+nvecc).(lvecp+mvecq+nvecr) is equal to

If veca, vecb, vecc are non coplanar vectors and vecp, vecq, vecr are reciprocal vectors, then (lveca+mvecb+nvecc).(lvecp+mvecq+nvecr) is equal to

If veca, vecb, vecc are non coplanar vectors and vecp, vecq, vecr are reciprocal vectors, then (lveca+mvecb+nvecc).(lvecp+mvecq+nvecr) is equal to

If veca,vecb, vecc are three vectors such that veca + vecb +vecc =vec0, |veca| =1 |vecb| =2, | vecc| =3 , then veca.vecb + vecb .vecc +vecc + vecc.veca is equal to

veca.(vecbxxvecc) is called the scalar triple product of veca,vecb,vecc and is denoted by [veca vecb vecc]. If veca, vecb, vecc are cyclically permuted the vaslue of the scalar triple product remasin the same. In a scalar triple product, interchange of two vectors changes the sign of scalar triple product but not the magnitude. in scalar triple product the the position of the dot and cross can be interchanged privided the cyclic order of vectors is preserved. Also the scaslar triple product is ZERO if any two vectors are equal or parallel. [veca+vecb vecb+vecc vecc+veca] is equal to (A) 2[veca vecb vecc] (B) 3[veca,vecb,vecc] (C) [veca,vecb,vecc] (D) 0

If vecA=vecB+vecC and vecA,vecB,vecC have scalar magnitudes of 5, 4, 3 units respectively then the angle between vecA and vecC is

Let veca,vecb and vecc be three vectors. Then scalar triple product [veca vecb vecc] is equal to