If `A B Ca n dA ' B ' C` are two triangles and `G , G '` be their centriods, prove that ` vec AA '+ vec B B '+ vec CC '=3 vec G G '`

If G is the centroid of a triangle ABC, prove that vec GA+vec GB+vec GC=vec 0

For any two vectors vec a and vec b prove that | vec a + vec b | <= | vec a | + | vec b |

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)

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 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

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

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

If a, b and c are any three vectors, then prove that vec a.(vec b+vec c)=(vec a.vec b)+(vec a.vec c)

If vec A, vec B and vec C are vectors such that | vec B | - | vec C | * Prove [(vec A + vec B) xx (vec A + vec C)] xx (vec B + vec C) * (case B + case C) = 0

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]