सिद्ध कीजिए कि `(vecaxxvecb)xx(veccxxvecd)=[vecavecbvecd]vecc-[vecavecbvecc]vecd`

For any four vectors veca , vecb , vecc , vecd we have (vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca .

Assetion: (vecaxxvecb)xx(veccxxvecd)=[veca vecc vecd]vecb-[vecb vecc vecd]veca Reason: (vecaxxvecb)xxvecc=(veca.vecc)vecb-(vecb.vecc)veca (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.

Assetion: (vecaxxvecb)xx(veccxxvecd)=[veca vecc vecd]vecb-[vecb vecc vecd]veca Reason: (vecaxxvecb)xxvecc=(veca.vecc)vecb-(vecb.vecc)veca (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.

Prove that : [vecavecbvecc+vecd]=[vecavecbvecc]+[vecavecbvecd] .

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc) Now answer the following question: (vecaxxvecb).(veccxxvecd) is equal to (A) veca.(vecbxx(veccxxvecd)) (B) |veca|(vecb.(veccxxvecd)) (C) |vecaxxvecb|.|veccxxvecd| (D) none of these

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc) Now answer the following question: {(vecaxxvecb).xxvecc}.vecd would be equal to (A) veca.(vecbxx(veccxxvecd)) (B) ((vecaxxvecc)xxvecb).vecd (C) (vecaxxvecb).(veccxxvecd) (D) none of these

Prove that: (vecaxxvecb)xx(veccxxvecd)+(vecaxxvecc)xx(vecd xx vecb)+(vecaxxvecd)xx(vecbxxvecc) = -2[vecb vecc vecd] veca

Prove that: (vecaxxvecb)xx(veccxxvecd)+(vecaxxvecc)xx(vecd xx vecb)+(vecaxxvecd)xx(vecbxxvecc)=2[vecb vecc vecd] veca

Prove that: (vecaxxvecb)xx(veccxxvecd)+(vecaxxvecc)xx(vecd xx vecb)+(vecaxxvecd)xx(vecbxxvecc) = -2[vecb vecc vecd] veca