`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

If veca+2vecb+3vecc=0 , then vecaxxvecb+vecbxxvecc+veccxxveca=

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

If veca , vecb , vecc are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is 1/2 ​ [ veca × vecb + vecb × vecc + vecc × veca ] . Also deduce the condition for collinearity of the points A, B and C.

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

For three vectors veca+vecb+vecc=0 , check if (vecaxxvecb)=(vecbxxvecc)=(veccxxveca)

Let A( veca ), B ( vecb ) and C( vecc ) be the vertices of the triangle with circumcenter at origin. Assertion: The nine point centre wil be ((veca+vecb+vecc)/2) , Reason: Centroid of /_\ABC is ((veca+vecb+vecc)/3) and nine point centre is the middle point of the line segment joining circumcentre and orthocentre. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If veca,vecb,vecc are coplanar then show that vecaxxvecb, vecbxxvecc and veccxxveca are also coplanar.

For any three vectors veca, vecb, vecc the vector (vecbxxvecc)xxveca equals