Property 3&4: `[[veca+vecb, vecc, vecd]] = [[veca, vecc, vecd]] + [[vecb, vecc, vecd]]` and right and left handed system

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

If [(2veca+4vecb,vecc,vecd)]=lamda[(veca,vecc,vecd)]+mu[(vecb,vecc,vecd)] , then lamda+mu=

If veca, vecb, vecc, vecd are coplanar vectors, then (vecaxxvecb)xx(veccxxvecd)=

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

Statement 1: veca, vecb and vecc arwe three mutually perpendicular unit vectors and vecd is a vector such that veca, vecb, vecc and vecd are non- coplanar. If [vecd vecb vecc] = [vecdvecavecb] = [vecdvecc veca] = 1, " then " vecd= veca+vecb+vecc Statement 2: [vecd vecb vecc] = [vecd veca vecb] = [vecdveccveca] Rightarrow vecd is equally inclined to veca, vecb and vecc .

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 are three non zero vectors such that veca xx vecb = vecc and vecbxx vecc = veca. Prove that veca, vecb and vecc are mutually at right angles and |vecb|=1 and |vecc| =|veca|

If veca,vecb,vecc are unity vectors such that vecd=lamdaveca+muvecb+gammavecc then gamma 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])

Prove that vecaxx{vecbxx(veccxxvecd)}=(vecb.vecd)(vecaxxvecc)-(vecb.vecc)(vecaxxvecd)

If the vectors veca, vecb, vecc, vecd are any four vectors, then (vecaxxvecb).(veccxxvecd) is equal to