If `vecaxxvecb=vecaxxvecc,vecane0` and `vecbnevecc`, prove that `vecb=vecc+lamdaveca`.

If veca,vecb,vecc,vecd are four distinct vectors satisfying the conditions vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxd then prove that veca.vecb+vecc.vecd!=veca.vecc+vecb.vecd

If vecaxxvecb=vecc,vecb xx vecc=veca, where vecc != vec0, then

If veca,vecb,vecc are three such that vecaxxvecb=vecc, vecbxxvecc=veca and veccxxveca=vecb , show that veca,vecb,vecc foem an orthogonal righat handed triad of unit vectors.

If veca.vecb=0 and vecaxxvecb=0 prove that veca=vec0 or vecb=vec0 .

If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd then (A) (veca-vecd)=lamda(vecb-vecc) (B) veca+vecd=lamda(vecb+vecc) (C) (veca-vecb)=lamda(vecc+vecd) (D) none of these

If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that (veca-vecd) is parallel to (vecb-vecc) .

If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc), Where veca, vecb and vecc and any three vectors such that veca.vecb=0,vecb.vecc=0, then veca and vecc are

If vecaxx(vecaxxvecb)=vecbxx(vecbxxvecc) and veca.vecb!=0 , then [(veca,vecb,vecc)]=

If vecaxxvecb=vecc and vecbxxvecc=veca , show that veca,vecb,vecc are orthogonal in pairs. Also show that |vecc|=|veca| and |vecb|=1

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|