` vec a , vec b` and ` vec c` are the position vectors of points `A ,B` and `C` respectively, prove that : ` vec ax vec b+ vec bx vec c+ vec cx vec a` is vector perpendicular to the plane of triangle `A B Cdot`

If vec(a), vec(b), vec(c ) are position vectors of non - collinear points A, B and C respectively, show that : vec(a)xx vec(b)+vec(b)xx vec(c )+vec(c )xx vec(a) is perpendicular to the plane ABC.

If vec a,vec b,vec c are the position vectors of points A,B,C and D respectively such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 then D is the

If vec a,vec b,vec c are position vectors o the point A,B, and C respectively,write the value of vec AB+vec BC+vec AC

If vec(b) and vec(c) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD) = 4 vec(BC) is

If vec(b) and vec(c ) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD)= 4 vec(BC) is

If vec a,vec b and vec c are the position vectors of the vertices A,B and C respect ively,of bigoplus ABC , prove that the perpendicular distance of the vertedx A from the base BC of the triangle ABC is (|vec a xxvec b+vec b xxvec c+vec c xxvec a|)/(|vec c-vec b|)

If vec a,vec b,vec c are three vectors such that vec a+vec b+vec c=vec 0, then prove that vec a xxvec b=vec b xxvec c=vec c xxvec a

Prove that the points A,B and C with position vectors vec a,vec b and vec c respectively are collinear if and only if vec a xxvec b+vec b xxvec c+vec c xxvec a=vec 0

For any three vectors vec a, vec b, vec c, (vec a-vec b) * (vec b-vec c) xx (vec c-vec a) is equal to

For any three vectors vec a;vec b;vec c find [vec a+vec b;vec b+vec c;vec c+vec a]