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

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

If the vectors veca, vecb, vecc, vecd are any four vectors, then (vecaxxvecb).(veccxxvecd) is equal to

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|

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|

If veca,vecb,vecc,vecd are unit vectors such that veca.vecb=1/2 , vecc.vecd=1/2 and angle between veca xx vecb and vecc xx vecd is pi/6 then the value of |[vecavecbvecd]vecc-[vecavecbvecc]vecd|=

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

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]