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`

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

vec a,vec b and vec c are the position vectors of points A,B and C respectively,prove that: vec a_(vec a)xvec b+vec bxvec c+vec cxvec a is vector perpendicular to the plane of triangle ABC.

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

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

If O A B C is a tetrahedron where O is the orogin anf A ,B ,a n dC are the other three vertices with position vectors, vec a , vec b ,a n d vec c respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector (a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c]) .

vec a,vec b,vec c,vec d are the position vectors of the four distinct points A,B,C, D respectively.If vec b-vec a=vec c-vec d, then show that ABCD is a parallelogram.

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 and vec d are the position vectors of the vertices of a cyclic quadrilateral ABCD prove that (|vec a xxvec b+vec b xxvec d+vec d xxvec a|)/((vec b-vec a)*(vec d-vec a))+(|vec b xxvec c+vec c xxvec d+vec d xxvec b|)/((vec b-vec c)*(vec d-vec c))=

Prove that [vec a,vec b,vec c+vec d]=[vec a,vec b,vec c]+[vec a,vec b,vec d]