Find vector `vecr` if `vecr.veca=m and vecrxxvecb=vecc, where veca.vecb!=0`

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 vec r xx veca = vec b xx veca and vecc vecr=0 , where veca.vecc ne 0 , then veca.vecc(vecr xx vecb)+(vecb.vecc)(veca xx vecr) is equal to __________.

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

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:

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 .

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)]=

If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr satisfying vecr.veca=vecr.vecb=vecr.vecc=1 , is

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 _______.

The plane contaning the two straight lines vecr=veca+lamda vecb and vecr=vecb+muveca is (A) [vecr vecas vecb]=0 (B) [vecr veca veca xxvecb]=0 (C) [vecr vecb vecaxxvecb]=0 (D) [vecr veca+vecb vecaxxvecb]=0

If vecb is not perpendicular to vecc . Then find the vector vecr satisfying the equation vecr xx vecb = veca xx vecb and vecr. vecc=0