Show that `[veca vecb vecc]\^2=|(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|`

If veca=hati+hatj+hatk,hatb=hati-hatj+hatk,vecc=hati+2hatj-hatk , then find the value of |{:(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc):}|

If veca, vecb, vecc are three given non-coplanar vectors and any arbitrary vector vecr in space, where Delta_(1)=|{:(vecr.veca,vecb.veca,vecc.veca),(vecr.vecb,vecb.vecb,vecc.vecb),(vecr.vecc,vecb.vecc,vecc.vecc):}|,Delta_(2)=|{:(veca.veca,vecr.veca,vecc.veca),(veca.vecb,vecr.vecb,vecc.vecb),(veca.vecc,vecr.vecc ,vecc.vecc):}| Delta_(3)=|{:(veca.veca,vecb.veca,vecr.veca),(veca.vecb,vecb.vecb,vecr.vecb),(veca.vecc,vecb.vecc,vecr.vecc):}|, Delta=|{:(veca.veca,vecb.veca,vecc.veca),(veca.vecb,vecb.vecb,vecc.vecb),(veca.vecc,vecb.vecc,vecc.vecc):}|, "then prove that " vecr=(Delta_(1))/Deltaveca+(Delta_(2))/Deltavecb+(Delta_(3))/Deltavecc

If |{:(veca,vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(veca.vecc,vecb.vecc,veca.vecc)| where veca, vecb,vecc are coplanar then:

If the vectors veca, vecb, and vecc are coplanar show that |(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0

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

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

If V is the volume of the parallelepiped having three coterminous edges as veca,vecb and vecc , then the volume of the parallelepiped having three coterminous edges as vecalpha = (veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc , vecbeta=(vecb.veca)veca+(vecb.vecb)+(vecb.vecc)vecc and veclambda=(vecc.veca)veca+(vecc.vecb)vecb+(vecc.vecc)vecc is

The vectors veca and vecb are not perpendicular and vecc and vecd are two vectors satisfying : vecbxxvecc=vecbxxvecd and veca.vecd=0. Then the vecd is equal to (A) vecc+(veca.vecc)/(veca.vecb)vecb (B) vecb+(vecb.vecc)/(veca.vecb)vecc (C) vecc-(veca.vecc)/(veca.vecb)vecb (D) vecb-(vecb.vecc)/(veca.vecb)vecc

If veca,vecb,vecc are coplanar vectors , then show that |{:(veca,vecb,vecc),(veca*veca,veca*vecb,veca*vecc),(vecb*veca,vecb*vecb,vecb*vecc):}|=vec0

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 (vecaxxveca\')+(vecbxxvecb\')+(veccxxvecc\') is (A) veca+vecb+vecc (B) veca\'+vecb\'+vecc\' (C) 0 (D) none of these