If `veca,vecb and vecc` are three mutually perpendicular unit vectors then `(vecr.veca)veca+(vecr.vecb)vecb+(vecr.vecc)vecc=` (A) `([veca vecb vecc]vecr)/2` (B) `vecr` (C) `2[veca vecb vecc]` (D) none of these

If veca and vecb are mutually perpendicular unit vectors, vecr is a vector satisfying vecr.veca =0, vecr.vecb=1 and (vecr veca vecb)=1 , then vecr is:

If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr satisfying vecr.veca=vecr.vecb=vecr.vecc=1 , is

The scalar vecA.(vecB+vecC)xx(vecA+vecB+vecC) equals (A) 0 (B) [vecA vecB vecC]+[vecB vecC vecA] (C) [vecA vecB vecC] (D) none of these

Let veca, vecb and vecc are three mutually perpendicular unit vectors and a unit vector vecr satisfying the equation (vecb -vecc)xx(vecr xx veca)+(vecc -veca)xx(vecr xx vecb)+(veca-vecb)xx(vecr xx vecc)=0, then vecr is

If veca,vecb and vecc are non coplnar and non zero vectors and vecr is any vector in space then [vecc vecr vecb]veca+pveca vecr vecc] vecb+[vecb vecr veca]c= (A) [veca vecb vecc] (B) [veca vecb vecc]vecr (C) vecr/([veca vecb vecc]) (D) vecr.(veca+vecb+vecc)

If veca, vecb, vecc are any three non coplanar vectors, then (veca+vecb+vecc).(vecb+vecc)xx(vecc+veca)

If veca, vecb, vecc and veca', vecb', vecc' form a reciprocal system of vectors then veca.veca'+vecb.vecb'+vecc.vecc'=

If vecb and vecc are any two orthogonal unit vectors and veca is any vector, then (veca.vecb)vecb + (veca.vecc)vecc + (veca.(vecb xx vecc))/|vecb xx vecc|^(2) (vecb xx vecc) =

If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc0 is (A) |[veca vecb vecc]| (B) |vecr| (C) |[veca vecb vecr]vecr| (D) none of these

If veca,vecb and vecc are three non coplanar vectors and vecr is any vector in space, then (vecaxxvecb)xx(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)= (A) [veca vecb vecc] (B) 2[veca vecb vecc]vecr (C) 3[veca vecb vecc]vecr (D) 4[veca vecb vecc]vecr