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

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.

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 .

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

If vectors, vecb, vecc and vecd are not coplanar, the prove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

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

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,vecc and vecd are unit vectors such that (vecaxxvecb).(veccxxvecd)=1 and veca.vecc=1/2 then (A) veca,vecb,vecc are non coplanar (B) vecb,vecc, vecd are non coplanar (C) vecb, vecd are non paralel (D) veca, vecd are paralel and vecb, vecc are parallel