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, 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|)

Prove that: [vecaxxvecb ,vecbxxvecc ,veccxxveca] = [veca vecb vecc]^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 veca, vecb, vecc are three vectors, then [(vecaxxvecb, vecbxxvecc, veccxxveca)]=

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

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.

Let veca,vecb and vecc be the three non-coplanar vectors and vecd be a non zero vector which is perpendicular to veca+vecb+vecc and is represented as vecd=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca) . Then,

Prove that veca,vecb,vecc are coplanar iff vecaxxvecb,vecbxxvecc,veccxxveca are coplanar

If veca, vecb, vecc are three non-coplanar vetors represented by non-current edges of a parallelopiped of volume 4 units, then the value of (veca+vecb).(vecbxxvecc)+(vecb+vecc).(veccxxveca)+(vecc+veca).(vecaxxvecb) , is