Let ` vec a , vec b ,a n d vec c` be non-coplanar vectors and let the equation ` vec a^' , vec b^' , vec c '` are reciprocal system of vector ` vec a , vec b , vec c ,` then prove that ` vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c '` is a null vector.

Let vec a, vec b and vec c, are non-coplianar vectors such that [(vec a xxvec b) * vec c] = | vec a || vec b || vec c | then

If vec a, vec b, vec c are three vectors such that | vec b | = | vec c | then {(vec a + vec b) xx (vec a + vec c)} xx {(vec b xxvec c)} * (vec b + vec c) =

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])

Let vec a , vec b , vec c be the three unit vectors such that vec a+5 vec b+3 vec c= vec0 , then vec a. ( vec bxx vec c) is equal to

If the three vectors vec a,vec b,vec c are coplanar, prove that the vectors vec a+vec b,vec b+vec c and vec c+vec a are also coplanar.

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 c are the three coplanar vectors and if vec r*vec a=vec r*vec b=vec r*vec c=0 then prove that vec r is a zero vector

vec a, vec b ,, vec c are coplanar vectors, prove that vec a, vec b, vec cvec with a, vec with b, vec a, vec with bvec a, vec bvec b, vec b, vec a] | = 0

Let vec a, vec b, vec c be three nonzero vectors such that vec a + vec b + vec c = vec 0 and lambdavec b xxvec a + vec b xxvec c + vec c xxvec a = 0 then lambda is

If vec a , vec b ,a n d vec c be three non-coplanar vector and a^(prime),b^(prime)a n dc ' constitute the reciprocal system of vectors, then prove that vec r=( vec rdot vec a ') vec a+( vec rdot vec b^') vec b+( vec rdot vec c^') vec c vec r=( vec rdot vec a ') vec a '+( vec rdot vec b^') vec b '+( vec rdot vec c ') vec c '