Show by a numerical example and geometrically also that ` vec axx vec b= vec axx vec c` does not imply ` vec b= vec c`

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

Show that: vec a*(vec b+vec c)=vec a*vec b+vec a*vec c

Show that vec(a)xx vec(b)=vec(a)xx vec(c ) does not imply vec(b)=vec(c ) . Illustrate geometrically.

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

If for three non zero vectors vec a,vec b and vec cvec a*vec b=vec a.vec c and vec a xxvec b=vec a xxvec c, the show that vec b=vec c .

If a ,\ b represent the diagonals of a rhombus, then vec axx vec b= vec0 b. vec adot vec b=0 c. vec adot vec b=1 d. vec axx vec b= vec a

If vec a=a_1 hat i+a_2 hat j+a_3 hat k ,\ vec b=b_1 hat i+b_2 hat j+b_3 hat k\ a n d\ vec c=c_1 hat i+c_2 hat j+c_3 hat k , then verify that vec axx( vec b+ vec c)= vec axx vec b+ vec axx vec c

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

For any three vectors a b,c,show that vec a xx(vec b+vec c)+vec b xx(vec c+vec a)+vec c xx(vec a+vec b)=0