Show that the plane through the points `veca,vecb,vecc` has the equation `[vecr vecb vecc]+[vecr vecc veca]+[vecr veca vecb]=[veca vecb vecc]`

[ veca + vecb vecb + vecc vecc + veca ]=[ veca vecb vecc ] , then

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

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

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

Show that the points whose position vectors are veca,vecb,vecc,vecd will be coplanar if [veca vecb vecc]-[veca vecb vecd]+[veca vecc vecd]-[vecb vecc vecd]=0

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 and veca.vecb\'=veca.vecc\'=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

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

If veca,vecb,vecc are unity vectors such that vecd=lamdaveca+muvecb+gammavecc then lambda is equal to (A) ([veca vecb vecc])/([vecb veca vecc]) (B) ([vecb vecc vecd])/([vecb vecc veca]) (C) ([vecb vecd vecc])/([veca vecb vecc]) (D) ([vecc vecb vecd])/([veca vecb vecc])

if veca + vecb + vecc=0 , then show that veca xx vecb = vecb xx vecc = vecc xx veca .

If veca,vecb and vecc are non coplnar and non zero vectors and vecr is any vector in space then [vecc vecr vecb]veca+[veca vecr vecc] vecb+[vecb vecr veca]c= (A) [veca vecb vecc] (B) [veca vecb vecc]vecr (C) vecr/([veca vecb vecc]) (D) vecr.(veca+vecb+vecc)