`A B C D E` is pentagon, prove that ` vec A B` + ` vec B C` + ` vec C D` + ` vec D E+ vec E A` = ` vec0` ` vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C`

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

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

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)

In a regular hexagon A B C D E F ,\ A vec B=a ,\ B vec C= vec b\ a n d\ vec C D=c Then\ vec A E= a. vec a+ vec b+ vec c b. 2 vec a+ vec b+ vec c c. vec b+ vec c d. vec a+2 vec b+2 vec c

In a regualr hexagon ABCDEF, A vecB = vec a, B vec C = vecb and C vec D = vec c. " Then " A vec E =

If? B, c are three vectors such that | vec a | = 5, | vec b | = 12 and | vec c | = 13 and vec a + vec b + vec c = 0 then vec a * vec b + vec b * vec c + vec c * vec a

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

If vec a, vec b, vec c are unit vectors such that vec a + vec b + vec c = vec 0 find the value of vec a * vec b + vec b * vec c + vec c * vec avec a * vec b + vec b * vec c + vec c * vec a

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

Let vec a, vec b, vec c, vec d be unit vectors such that vec a * vec b + vec a * vec c + vec a * vec d + vec b * vec c + vec b * vec d + vec c * vec d = -2 Then [vec with bvec c] + [vec with bvec d] + [vec with cvec d] + [vec bvec cvec d] =