`vecaxxvecb` is not equal to `vecbxxveca`. Why ?

If vecb and vecc are two non-collinear such that veca ||(vecbxxvecc) . Then prove that (vecaxxvecb).(vecaxxvecc) is equal to |veca|^(2)(vecb.vecc)

vecrxxveca=vecbxxveca,vecrxxvecb=vecaxxvecb,vecanevec0,vecbnevec0,vecanelambdavecb and veca is not perpendicular to vecb , then find vecr in terms of veca and vecb .

[(vecaxxvecb) (veccxxvecd) (vecexxvecf)] is equal to (a) [vecavecbvecd][veccvecevecf]-[vecavecbvecc][vecdvecevecf] (b) [vecavecbvece][vecfveccvecd]-[vecavecbvecf][veceveccvecd] (c) [veccvecdveca][vecbvecevecf]-[vecavecdvecb][vecavecevecf] (d) [vecaveccvece][vecbvecdvecf]

If veca,vecb ,vecc are any three non- coplanar vectors then the equation [vecbxxvecc veccxxveca vecaxxvecb]x^(2) + [veca+vecb vecb+vecc vecc+veca] x+1 +[vecb-vecc vecc -veca veca -vecb] =0 has roots (A) real and distinct (B) real (C) equal (D) imaginary

If vecA=(1,1,1) and vecC=(0,1,-1) are given vectors then find a vector vecB satisfying equations vecAxxvecB=vecC and vecA.vecB=3

If veca, vecb and vecc are non- coplanar vecotrs, then prove that |(veca.vecd)(vecbxxvecc)+(vecb.vecd)(veccxxveca)+(vecc.vecd)(vecaxxvecb)| is independent of vecd where vecd is a unit vector.

Let the vectors vecaandvecb be such that |veca|=3and|vecb|=(sqrt(2))/(3) , then vecaxxvecb is a unit vector , if the angle between vecaandvecb is

If veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -hatk , " then " vecb is

If veca and vecb are two vectors, such that veca.vecbgt0 and |veca.vecb|=|vecaxxvecb| then the angle between the vectors veca and vecb is