If ` vec a ,\ vec b ,\ vec c` are three vectors such that ` vec adot vec b= vec adot vec c` then show that ` vec a=0\ or ,\ vec b=c\ or\ vec a_|_( vec b- vec c)dot`

If vec a ,\ vec b ,\ vec c are three vectors such that vec adot\ vec b= vec adot\ 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 vectors such that vec a+vec b+vec c=vec 0, then prove that vec a xxvec b=vec b xxvec c=vec c xxvec a

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 and vec c be any three vectors then show that vec a+(vec b+vec c)=(vec a+vec b)+vec c

If vec a,vec b, and vec c are three vectors such that vec a xxvec b=vec c,vec b xxvec c=vec a,vec c xxvec a=vec b then prove that |vec a|=|vec b|=|vec c|

If vec a, vec b, vec c are three mutually perpendicular vectors such that | vec a | = | vec b | = | vec c | then (vec a + vec b + vec c) * vec a =

If vec a,vec b,vec c are unit vectors such that vec a+vec b+vec c=vec 0, then write the value of vec a*vec b+vec b*vec c+vec c*vec a

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 vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is (pi)/(2), then

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