If ` vec a , vec ba n d vec c` are the position vectors of the vertices `A ,Ba n dC` respect ively, of ` A B C ,` prove that the perpendicular distance of the vertedx `A` from the base `B C` of the triangle `A B C` is `(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|)/(| vec c- vec b|)dot`

If vec a , vec ba n d vec c are the position vectors of the vertices A ,Ba n dC respectively, of A B C , prove that the perpendicular distance of the vertex A from the base B C of the triangle A B C is (| vec axx vec b+ vec bxx vec c+ vec cxx vec a|)/(| vec c- vec b|)dot

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|)

Show that perpendicular distance of the point vec c from the line joining vec a and vec b is (| vec bxx vec c+ vec cxx vec a+ vec axx vec b|)/(| vec b- vec a|)

If vec a ,\ vec b ,\ vec c are position vectors of the vertices A ,\ B\ a n d\ C respectively, of a triangle A B C ,\ write the value of vec A B+ vec B C+ vec C Adot

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

If vec a , vec b , vec ca n d vec d are the position vectors of the vertices of a cyclic quadrilateral A B C D , prove that (| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/((vec b- vec a).(vec d- vec a)) + (| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/((vec b- vec c).( vec d- vec c))=0dot

If vec a , vec b , vec ca n d vec d are the position vectors of the vertices of a cyclic quadrilateral A B C D , prove that (| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/(( vec b- vec a)dot( vec d- vec a))+(| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/(( vec b- vec c)dot( vec d- vec c))=0dot

For any three vectors a,b\ a n d\ c write the value of vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot

For any three vectors adotb\ a n d\ c write the value of vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2