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

Hence, show that veca.vecb+vecb.vecc+vecc.veca=(-3)/2 if veca+vecb+vecc=0 .

Prove that (veca xx vecb)^2=|(veca.veca,veca.vecb),(veca.vecb,vecb.vecb)| .

Show that if veca+vecb,vecb+vecc,vecc+veca are coplanar then veca,vecb,vecc are also coplanar.

veca,vecb,vecc are three non zero vectors such that vecaxxvecb=vecc,vecbxxvecc=veca .Prove that veca,vecb,vecc are mutually at right angle and |vecb|=1,|vecc|=|veca| .