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 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,vecb,vecc are the position vectors oif three non collinear points AS,B,C respectively, show that eperpendicular distance of C ferom the line through A and B is (|vecaxxvecb+vecbxxvecc+veccxxveca|)/(|vecb-veca|)

If veca+2vecb=3vecb=0, then vecaxxvecb+vecbxxvecc+veccxxveca= (A) 2(vecaxxvecb) (B) 6(vecbxxvecc) (C) 3(veccxxveca) (D) 0

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

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 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

Let veca,vecb,vecc be unit such that veca+vecb+vecc=vec0 . Which one of the following is correct? (A) vecaxxvecb=vecbxxvecc=veccxxveca=vec0 (B) vecaxxvecb=vecbxxvecc=veccxxveca!=vec0 (C) vecaxxvecb=vecbxxvecc=vecxxvecc!=vec0 (D) vecaxxvecb, vecbxxvecc, veccxxveca are mutually perpendicular