If `a(vecalpha xx vecbeta)xx(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=0` and at leasy one of a,b and c is non-zerp , then vector `vecalpha, vecbeta and gamma` are

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( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalpha)=0 and at least one of a ,ba n dc is nonzero, then vectors vecalpha, vecbetaa n d vecgamma are a. parallel b. coplanar c. mutually perpendicular d. none of these

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

if vecalpha||( vecbetaxx vecgamma) , then ( vecalphaxxbeta).(vecalphaxx vecgamma) equals to a. | vecalpha|^2( vecbeta.vecgamma) b. | vecbeta|^2( vecgamma. vecalpha) c. | vecgamma|^2( vecalpha. vecbeta) d. | vecalpha|| vecbeta|| vecgamma|

If vecalpha||(vecbxxvecgamma), then (vecalphaxxvecbeta).(vecalphaxxvecgamma)= (A) |vecalpha|^2(vecbeta.vecgamma) (B) |vecbeta|^2(vecgamma.vecalpha) (C) |vecgamma|^2(vecalpha.vecbeta) (D) |vecalpha||vecbeta||vecgamma|

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

If (veca xx vecb)xx vec c=veca xx (vecb xx vec c) , where veca, vecb and vec c are any three vectors such that veca*vecb ne 0, vecb*vec c ne 0 , then veca and vec c are :

Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vector such that r times a=b and r*a=1 , then

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

Let vecalpha = 3hati + hatj and beta= 2hati - hatj + 3hatk . If vecbeta = vecbeta_(1) - vecbeta_(2) , where vecbeta_(1) is parallel to vecalpha and vecbeta_(2) is perpendicular to vecalpha , then vecbeta_(1) xx vecbeta_(2) is equal to: