If `vecaxxvecb=veccxxvecd` and `vecaxxvecc=vecbxxvecd` then show that `veca-vecd` is parallel to `vecb-vecc`

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

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

STATEMENT-1 : If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd , then veca-vecd is perpendicular to vecb-vecc . And STATEMENT-2 : If vecP and vecQ are perpendicular then vecP.vecQ=0 .

Assertion: If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd the (veca-vecd) is perpendicular to (vecb-vecc) ., Reason : If vecp is perpendicular to vecq then vecp.vecq=0 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

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

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 veca.vecb=veca.vecc, vecaxxvecb=vecaxxvecc and veca!=vec0, then prove that vecb=vecc.

If veca, vecb, vecc and vecd ar distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.

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.

veca,vecb,vecc are non zero vectors. If vecaxxvecb=vecaxxvecc and veca.vecb=veca.vecc then show that vecb=vecc .