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:

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 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 :

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=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 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 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

Lines vecr xx vecb = veca xx vecb and vecr xx veca = vecb xx veca , where veca =hati + hatj, vecb = 2hati -hatk intersect at