If `a ,b ,c` are the lengths of sides, `B C ,C A` and `A B` of a triangle `A B C ,` prove that ` vec B C+ vec C A+ vec A B= vec O` and deduce that `a/(sinA)=b/(sinB)=c/(sinC)dot`

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If vec a + vec b + vec c = o, prove that vec a xxvec b = vec b xxvec c = vec c xxvec a

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

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

In a triangle OAC, if B is the mid point of side AC and vec O A= vec a , vec O B= vec b , then what is vec O C ?

If G is the centroid of Delta ABC and G' is the centroid of Delta A' B' C' " then " vec(A A)' + vec(B B)' + vec(C C)' =

If vec a,vec b,vec c be the vectors represented by theside sof a triangle,taken in order,then prove that vec a+vec b+vec c=vec 0

If vec a,vec b,vec c are the position vectors of the vertices A,B,C of a triangle ABC, show that the area triangle ABCis(1)/(2)|vec a xxvec b+vec b xxvec c+vec c xxvec a| Deduce the condition for points vec a,vec b,vec c to be collinear.

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

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n vec adot vec b+ vec bdot vec c+ vec cdot vec a=0 b. vec axx vec b= vec bxx vec c= vec cxx vec a c. vec adot vec b= vec bdot vec c= vec cdot vec a d. vec axx vec b+ vec bxx vec c+ vec cxx vec a=0