Prove that: `[vecaxxvecb ,vecbxxvecc ,veccxxveca]`=`[veca vecb vecc]^2`

Prove that [vecaxxvecb, vecbxxvecc, veccxxveca] = [[veca.veca, veca.vecb, veca.vecc], [veca.vecb,vecb.vecb, vecb.vecc], [veca.vecc, vecb.vecc,vecc.vecc]] = [veca, vecb, vecc]^2,Hence show that vectors vecaxxvecb, vecbxxvecc, veccxxveca are non-coplanar if and only if vectors veca, vecb, vecc are non-coplanar

Let veca,vecb, vecc be any three vectors, Statement 1: [(veca+vecb, vecb+vecc,vecc+veca)]=2[(veca, vecb, vecc)] Statement 2: [(vecaxxvecb, vecbxxvecc, veccxxveca)]=[(veca, vecb, vecc)]^(2)

If [(vecaxxvecb, vecbxxvecc, veccxxveca)]=lamda[(veca, vecb, vecc)]^(2) , then lamda is equal to

If [vecaxxvecb vecbxxvecc veccxxveca]=lamda [veca vecb vecc]^2 then lamda is equal to (A) 1 (B) 2 (C) 3 (D) 0

If veca,vecb, vecc and veca',vecb',vecc' are reciprocal system of vectors, then prove that veca'xxvecb'+vecb'xxvecc'+vecc'xxveca'=(veca+vecb+vecc)/([vecavecbvecc])

Prove that: [(vecaxxvecb)xx(vecaxxvecc)].vecd=[veca vecb vecc](veca.vecd)

Three points whose position vectors are veca,vecb,vecc will be collinear if (A) lamdaveca+muvecb=(lamda+mu)vecc (B) vecaxxvecb+vecbxxvecc+veccxxveca=0 (C) [veca vecb vecc]=0 (D) none of these

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc