If ` vec a ,\ vec b ,\ vec c` are three non coplanar vectors such that ` vec ddot vec a= vec ddot vec b= vec ddot vec c=0,` then show that `d` is the null vector.

If vec a ,\ vec b ,\ vec c are three non coplanar vectors such that vec d dot vec a= vec d dot vec b= vec d dot vec c=0, then show that d is the null vector.

If vec a , vec b , vec c are three non coplanar vectors such that vec adot vec a= vec d vec b= vec ddot vec c=0 , then show that vec d is the null vector.

If vec a,vec b,vec c are three non coplanar vectors such that vec a.vec a*vec a=vec dvec b=vec d*vec c=0 then show that vec d is the null vector.

If vec a , vec b , vec c are three non-coplanar vectors and vec d* vec a = vec d* vec b= vec d* vec c= 0 then show that vec d is zero vector.

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

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

If vec a ,\ vec b ,\ vec c are three vectors such that vec a. vec b= vec a.\ vec c and vec a\ xx\ vec b= vec a\ xx\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

If vec a, vec b, vec c are three non-coplanar vectors such that vec a + vec b + vec c = alphavec d and vec b + vec c + vec d = betavec a then vec a + vec b + vec c + vec d is equal to