सिद्ध कीजिए कि `[vecaxxvecb vecaxxvecc vecd]=[veca.vecd][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

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

For any four vectors veca , vecb , vecc , vecd we have (vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca .

[vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to (a) [veca vecb vecd] [vecc vece vecf]-[veca vecb vecc] [vecd vece vecf] (b) [veca vecb vece ] [vecf vecc vecd] - [veca vecb vecf] [vece vecc vecd] (c) [vecc vecd veca] [vecb vece vecf] - [veca vecd vecb] [vecavece vecf] (d) [veca vecc vece] [vecb vecd vecf]

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

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