Find `vecr` such that `tvecr+vecr+veca=vecb`.

If veca is perpendicular to vecb and vecr is a non-zero vector such that pvecr + (vecr.vecb)veca=vecc , then vecr is:

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

Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr.veca=0, |vecrxxvecb|=|vecr||vecb|,|vecrxxvecc|=|vecr||vecc| then [(veca, vecb, vecc)]=

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 .

Let veca = hati + hatj + hatk and let vecr be a variable vector such that vecr.hati, vecr.hatj and vecr.hatk are posititve integers. If vecr.veca le 12 , then the total number of such vectors is:

The vertices of a triangle have the position vectors veca,vecb,vecc and p( r) is a point in the plane of Delta such that: veca.vecb+ vecc.vecr = veca.vecc + vecb.vecr = vecb.vecc+veca.vecr then for the Delta , P is the:

If vecr is a unit vector such that vecr=x(vecbxxvecc)+y(veccxxveca)+z(vecaxxvecb) , then |(vecr.veca)(vecbxxvecc)+(vecr.vecb)(veccxxveca)+(vecr.vecc)(veccxxvecb)| is equal to

If veca and vecb are two given vectors and k is any scalar,then find the vector vecr satisfying vecr xx veca +k vecr=vecb .

If veca,vecb and vecc are non coplnar and non zero vectors and vecr is any vector in space then [vecc vecr vecb]veca+[veca 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 three non coplanar vectors such that vecr_1=veca-vecb+vecc,vecr_2=vecb+vecc-veca, vecr_3=vecc+veca+vecb,vecr=2veca-3vecb+3vecc if vecr=lamda_1 vecr_1+lamda_2vecr_2+lamda_3vecr_3 then (A) lamda_1=7/2 (B) lamda_1+lamda_2=3 (C) lamda_2+lamda_3=2 (D) lamda_1+lamda_2+lamda_3=4