If `a(vecalphaxxvecbeta)=b(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=vec0` and at least one of a,b and c is non zero then vectors `vecalpha, vecbeta, vecgamma` are (A) parallel (B) coplanar (C) mutually perpendicular (D) none of these

If a(vec alpha xxvec beta)+b(vec beta xxvec gamma)+c(vec gamma xxvec alpha)=0 and at least one of a,b and c is nonzero,then vectors vec alpha,vec beta and vec gamma are a.parallel b.coplanar c.mutually perpendicular d.none of these

If (vec a xxvec b)+beta(vec b xxvec c)+gamma(vec c xxvec a)=0 and at least of the numbers alpha,beta and gamma is non- zero,then the vectors vec a,vec b and vec c are

If a,b,c are three non-coplanar mutually perpendicular unit vectors,then [a,b,c] is

The vectors vec a,vec b,vec c,vec d are coplanar then

If alpha+beta+gamma= a vecdelta and vecbeta+vecgamma+vecdelta = b vecalpha and alpha, vecbeta, vecgamma are non coplanar and vecalpha is not parallel to vecdelta then vecalpha+vecbeta+vecgamma+vecdelta equals (A) avecalpha (B) bvecdelta (C) 0 (D) (a+b)vecgamma

If vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vecdelta=b vecalpha, vecalphaa n d vecdelta are non-colliner, then vecalpha+ vecbeta+ vecgamma+ vecdelta equals a. a vecalpha b. b vecdelta c. 0 d. (a+b) vecgamma

(vec a xxvec b)xx(vec b xxvec c)=vec b, where vec a,vec b, and vec c are nonzero vectors,then vec a,vec b, and vec c can be coplanar vec a,vec b, and vec c must be coplanar vec a,vec b, and vec c cannot be coplanar none of these

If veca,vecb,vecc are mutually perpendicular vector and veca=alpha(vecaxxvecb)+beta(vecbxxvecc)+gamma(veccxxveca) and [veca vecb vecc]=1 then vecalpha+vecbeta+vecgamma= (A) |veca|^2 (B) -|veca|^2 (C) 0 (D) none of these

A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, vecb=vecalpha+3vecbeta . If |vecalpha|=|vecbeta|=2 and angle between vecalpha and vecbeta is pi/3 then the length of a diagonal of the parallelogram is (A) 4sqrt(5) (B) 4sqrt(3) (C) 4sqrt(7) (D) none of these