Show that `[vecaxxvecb" "vecbxx vec c" "vec c xxveca]=[veca vecb vec c]^2`

Let veca, vecb and vec c be any three vectors; then prove that [[vecaxxvecb, vecbxxvecc, veccxxveca]] = [[veca, vecb, vecc]]^2

If [veca xx vecb vecb xx vec c vec c xx vec a] = lamda [veca vecb vec c ]^2 then lamda is equal to

For any three vectors veca,vecb,vec(c) prove that [vecbxxvec(c)" "vec(c)xxveca" "vecaxxvecb]=[vec(a)" "vecb" "vec(c)]^(2)

If [veca+vecb, vecb+vec c, vec c+veca]=8 then [veca, vecb, vec c] is

Show that [vecb, vec c, vecd]veca-[veca, vec c, vecd]vecb+[veca, vecb, vecd]vec c-[veca, vecb, vec c]vecd=0 .

Show that for any three vectors veca , vec b and vec c [ vec a + vec b, vecb + vec c , vec c + vec a ] =2[vec a , vec b , vecc] .

If vec a, vec b, vec c are three given vectors show that [ vec a + vecb + vec c , vecb + vec c , vec a + vec b + vec c ]=0.

Prove that : veca*(vecb+vec c)xx(veca+2vecb+3vec c)=[veca vecb vec c]

Let veca , vecb, vec c be three non coplanar vectors , and let vecp , vecq " and " vec r be the vectors defined by the relation vecp = (vecb xx vec c )/([veca vecb vec c ]), vec q = (vec c xx vec a)/([veca vecb vec c ]) " and " vec r = (vec a xx vec b)/([veca vecb vec c ]) Then the value of the expension (vec a + vec b) .vec p + (vecb + vec c) .q + (vec c + vec a) . vec r is equal to

For any three vectors veca , vec b , vec c show that vecaxx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)= vec0