`veca,vecb,vecc` are the position vectors of vertices A, B, C respectively of a paralleloram, ABCD, ifnd the position vector of D.

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, vecb, vecc, vecd are the position vectors of points A, B, C and D , respectively referred to the same origin O such that no three of these points are collinear and veca+vecc=vecb+vecd , then prove that quadrilateral ABCD is a parallelogram.

If veca & vecb are the position vectors of A & B respectively and C is a point on AB produced such that AC=3AB then the position vector of C is:

In a DeltaABC , the sides BC, CA and AB are consecutive positive integers in increasing order. Let veca, vecb and vecc are position vectors of the vertices A, B and C respectively. If (vecc-veca).(vecb-vecc)=0 , then the value of |veca xx vecb+vecbxx vecc+vecc xxveca| is equal to

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 veca,vecb,vec c are position vectors of the non- collinear points A, B, C respectively, the shortest distance of A from BC is

If veca,vecb,vecc and vecd are the position vectors of the vertices of a cycle quadrilateral ABCD, prove that (|vecaxxvecb+vecb xxvecd+vecd xxveca|)/((vecb-veca).(vecd-veca))+(|vecbxxvecc+veccxxvecd+vecd+vecd xx vecb|)/((vecb-vecc).(vecd-vecc))

If veca+2vecb+3vecc, 2veca+8vecb+3vecc, 2veca+5vecb-vecc and veca-vecb-vecc be the positions vectors A,B,C and D respectively, prove that vec(AB) and vec(CD) are parallel. Is ABCD a parallelogram?