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 a,b,c are the lengths of sides,BC,CA and AB of a triangle ABC, prove that vec BC+vec CA+vec AB=vec O and deduce that (a)/(sin A)=(b)/(sin B)=(c)/(sin C) .

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

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 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 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 veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

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

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

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)