`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 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+2hatj-hatk, vecb=hati-hatj and vecc=hati-hatj-hatk be three given vectors. If vecr is a vector such that vecr xx veca=vecc xx veca and vecr*vecb=0 , then vecr*veca is equal to _______.

If veca vecb be any two mutually perpendiculr vectors and vecalpha be any vector then |vecaxxvecb|^2 ((veca.vecalpha)veca)/(veca|^2)+|vecaxvecb|^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

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

Let vecq and vecr be non - collinear vectors, If vecp is a vector such that vecp.(vecq+vecr)=4 and vecp xx(vecq xx vecr)=(x^(2)-2x+9)vecq" then " +(siny)vecr (x, y) lies on the line

Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |veca|= sqrt3 and |vecb| = sqrt2

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 vecd 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 :