`A(veca),B(vecb),C(vecc)` are the vertices of the triangle ABC and `R(vecr)` is any point in the plane of triangle ABC , then `r.(vecaxxvecb+vecbxxvecc+veccxxveca)` is always equal to

A (veca), B (vecb) and C (vecc) are the vertices of triangle ABC and R(vecr) is any point in the plane of triangle ABC, then vecr. (veca xx vecb + vecb xx vecc + vecc xx veca ) is always equal to

If veca, vecb, vecc are three vectors, then [(vecaxxvecb, vecbxxvecc, veccxxveca)]=

If 4veca+5vecb+9vecc=0 " then " (vecaxxvecb)xx[(vecbxxvecc)xx(veccxxveca)] is equal to

If 4veca+5vecb+9vecc=vec0 then (vecaxxvecb).{(vecbxxvecc)xx(veccxxveca)} is equal to

If veca , vecb, vecc are the position vectors of the vertices. A,B,C of a triangle ABC. Then the area of triangle ABC is

Prove that: [vecaxxvecb ,vecbxxvecc ,veccxxveca] = [veca vecb vecc]^2

If veca+vecb+vecc=0 , prove that (vecaxxvecb)=(vecbxxvecc)=(veccxxveca)

If veca, vecb and vecc are the position vectors of vertices A,B,C of a Delta ABC, show that the area of triangle ABC is 1/2| veca xx vecb + vecbxx vec c+vec c xx veca|. Deduce the condition for points veca, vecb and vecc to be collinear.

If veca,vecb,vecc be three vectors such that [veca vecb vec c]=4 then [vecaxxvecb vecbxxvecc veccxxveca] is equal to