Let the vectors `veca,vecb,vecc` be the position vectors of the vertices P,Q,R respectively of a triangle. Which of the following represents the area of the triangle? (A) `1/2|vecaxxvecb|` (B) `1/2|vecbxxvecc|` (C) `1/2 |veccxxveca|` (D) `1/2|vecaxxvecb+vecbxxvecc+veccxxveca|`

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 and vecc are the position vectors of the vertices A,B and C. respectively , of triangleABC . Prove that the perpendicualar distance of the vertex A from the base BC of the triangle ABC is (|vecaxxvecb+vecbxxvecc+veccxxveca|)/(|vecc-vecb|)

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

The vector (veca-vecb)xx(veca+vecb) is equal to (A) 1/2 (vecaxxvecb) (B) vecaxxvecb (C) 2(veca+vecb) (D) 2(vecaxxvecb)

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

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 are the position vectors of A,B,C respectively prove that vecaxxvecb+vecbxxvecc+veccxxveca is a vector perpendicular to the plane ABC.

If vector veca lies in the plane of vectors vecb and vecc which of the following is correct? (A) veca.(vecbxxvecc)=-1 (B) veca.(vecbxxvecc)=0 (C) veca.(vecbxxvecc)=1 (D) veca.(vecbxxvecc)=2

If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively of a triangle ABC then (A) veca.(vecbxxvecc)=vec0 (B) vecaxx(vecbxvecc)=vec0 (C) veca.vecb=vecc=vecc=veca.a!=0 (D) vecaxxvecb+vecbxxvecc+veccxxvecavec0

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: The value of sin(theta/2) is (A) 1/2 |veca-vecb| (B) 1/2|veca+vecb| (C) |veca-vecb| (D) |veca+vecb|