`vecalpha` and `vecbeta` are two unit vectos and `vecr` is a vector such that `vecr.vecalpha=0` and `sqrt(2)(vecrxxvecbeta)=3(vecrxxvecalpha)-vecbeta`, then `(1)/(|vecr|^(2))` equal

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 and vecb be any two mutually perpendiculr vectors and vecalpha be any vector then |vecaxxvecb|^2 ((veca.vecalpha)veca)/(|veca|^2)+|vecaxxvecb|^2 ((vecb.vecalpha)vecb)/(|vecb|^2)-|vecaxxvecb|^2vecalpha= (A) |(veca.vecb)vecalpha|(vecaxxvecb) (B) [veca vecb vecalpha](vecbxxveca) (C) [veca vecb vecalpha](vecaxxvecb) (D) none of these

If veca and vecb are othogonal unit vectors, then for a vector vecr non - coplanar with veca and vecb vector vecr xx veca is equal to

Let veca=-hati-hatk,vecb =-hati + hatj and vecc = i + 2hatj + 3hatk be three given vectors. If vecr is a vector such that vecr xx vecb = vecc xx vecb and vecr.veca =0 then find the value of vecr .vecb .

If veca and vec b are non-zero, non-collinear vectors such that |veca|=2, veca*vecb=1 and angle between veca and vec b is (pi)/(3) . If vecr is any vector such that vecr*veca=2, vecr*vecb=8, (vec r+2veca-10vecb)*(vecaxxvecb)=4sqrt(3) and satisfy to vecr+2veca-10vecb=lambda(veca xx vec b) , then lambda is equal to : (a) 1/2 (b) 2 (c) 1/4 (d) none of these

If vec aa n d vec b are non-collinear vectors, find the value of x for which the vectors vecalpha=(2x+1) vec a- vec b""a n d"" vecbeta=(x-2)"" vec a+ vec b are collinear.

Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalpha)/(| vecalphaxx vecbeta|^2)+([ vec Rdot( vecalphaxx( vecalphaxx vecbeta))] vecbeta)/(| vecalphaxx vecbeta|^2)=([ vec R vecalpha vecbeta]( vecalphaxx vecbeta))/(| vecalphaxx vecbeta|^2)

Statement 1: Let vecr be any vector in space. Then, vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk Statement 2: If veca, vecb, vecc are three non-coplanar vectors and vecr is any vector in space then vecr={([(vecr, vecb, vecc)])/([(veca, vecb, vecc)])}veca+{([(vecr, vecc, veca)])/([(veca, vecb, vecc)])}vecb+{([(vecr, veca, vecb)])/([(veca, vecb, vecc)])}vecc

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 vecr and vecs are non-zero constant vectors and the scalar b is chosen such that |vecr+bvecs| is minimum, then the value of |bvecs|^(2)+|vecr+bvecs|^(2) is equal to