For any four vectors prove that
`(vecbxxvecc).(veca xxvecd)+(vecc xxveca).(vecbxxvecd)+(vecaxxvecb).(veccxxvecd)=0`

Prove that: (vecb xx vecc).(vecaxxvecd)+(veccxxveca).(vecbxxvecd)+(vecaxxvecb).(veccxxvecd)=0

If veca+vecb+vecc=0 , prove that (vecaxxvecb)=(vecbxxvecc)=(veccxxveca)

For any three vectors veca,vecb,vecc their product would be a vector if one cross product is folowed by other cross product i.e (vecaxxvecb)xxvecc or (vecbxxvecc)xxveca etc. For any four vectors veca,vecb,vecc,vecd the product would be a vector with the help of sequential cross product or by cross product of two vectors obtained by corss product of two pair i.e. (vecaxx(vecbxxvecc))xxvecd or (vecaxxvecb)xx(veccxxvecd). (vecaxxvecb)xx(veccxxvecd0 is a vector (A) along the line off intersection of two planes containing veca,vecb and vecc,vecd (B) perpendicular to plane containing veca,vecb and vecc,vecd (C) parallel to the plane containing veca,vecb and vecc,vecd (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).(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

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).(vecxxvecd) is equal to (A) (vecaxxvecd).(vecbxxvecc) (B) (vecbxxveca).(veccxxvecd) (C) (vecdxxvecc).(vecbxxveca0 (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).(vecxxvecd) is equal to (A) veca.(vecbxx(vecxxvecd)) (B) |veca|(vecb.(veccxxvecd)) (C) |vecaxxvecb|.|veccxxvecdD| (D) none of these

For any three vectors veca,vecb,vecc their product would be a vector if one cross product is folowed by other cross product i.e (vecaxxvecb)xxvecc or (vecbxxvecc)xxveca etc. For any four vectors veca,vecb,vecc,vecd the product would be a vector with the help of sequential cross product or by cross product of two vectors obtained by corss product of two pair i.e. (vecaxx(vecbxxvecc))xxvecd or (vecaxxvecb)xx(veccxxvecd). (vecaxxvecb)xx(veccxxvecd) would be a (A) equally inclined with veca,vecb, vecc, vecd (B) perpendicular with (vecaxxvecb)xxvecc and vecc (C) equally inclined with vecaxxvecb and veccxxvecd (D) none of these

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]