If `vec axxvec b`=`vec bxxvec c`=`vec cxxvec a` then `vec a+vec b+vec c` =

If vec axxvec b=vec b xxvec c != vec 0 , then show that vec a+vec c= k vec b where k is a scalar.

Let vec a,vec b, and vec c and vec a',vec b',vec c ,are reciprocal system of vectors,then prove that vec a'xxvec b'+vec b xxvec c'+vec c'xxvec a'=(vec a+vec b+vec c)/([vec avec bvec c])

If vec axx vec b= vec cxxvec d and vec axxvec c= vec bxxvec d, vec a ne vec d, vec b ne vec c then show that vec b- vec c is parallel to vec a-vec d

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

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 | =

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

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) a. [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]