Answer to Question #12463 in Analytic Geometry for john.george.milnor

Question

Prove that double vector product of three complanar vertors is zero

Answer 1

Let we have
A=tC
Then
[[A,B],C]=[[tC,B],C]=t[[C,B],C]=-t(C(C,B)-B(C,C))=t(B*|C|^2-C*|C|*|B|*cos(C^B))=t|C|*(B*|C|-C*|B|*cos(C^B))=0