Property 2: `[[k veca, vecb, vecc]] = k[[veca, vecb, vecc]]`

For three non - zero vectors veca, vecb and vecc , if [(veca, vecb , vecc)]=4 , then [(vecaxx(vecb+2vecc), vecbxx(vecc-3veca), vecc xx(3veca+vecb))] is equal to

Property 2 & 3: veca.vecb'=veca.vecc'=vecb.vecc'=vecc.veca'=0 and [[veca, vecb,vecc]][[veca',vecb',vecc']]=1

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . [veca,vecb,vecc]-(veca\'xxvecb\')+(vecb\'xxvec\')+(vecc\'xxveca\')= (A) veca+vecb+vecc (B) veca+vecb-vecc (C) 2(veca+vecb+vecc) (D) 3(veca\'+vecb\'+vecc\')

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)

Prove that [veca+vecb, vecb+vecc ,vecc+veca]=2[veca vecb vecc]

Prove that [veca+vecb vecb+vecc vecc+veca]=2[vecavecbvecc]

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of [veca\' vecb\' vecc\']^-1 is (A) 2[veca vecb vecc] (B) [veca,vecb,vecc] (C) 3[veca vecb vecc] (D) 0

For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc = |veca||vecb||vecc| holds if and only if

For three vectors veca, vecb and vecc , If |veca|=2, |vecb|=1, vecaxxvecb=vecc and vecbxxvecc=veca , then the value of [(veca+vecb,vecb+vecc,vecc+veca)] is equal to

Statement 1: If V is the volume of a parallelopiped having three coterminous edges as veca, vecb , and vecc , then the volume of the parallelopiped having three coterminous edges as vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc is V^(3) Statement 2: For any three vectors veca, vecb, vecc |(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)