If ` vec x. vec a=0, vec x. vec b=0` and `vec x. vec c=0` for some non-zero vector ` vec x` , then prove that `[ vec a vec b vec c]=0.`

Let vec r be a non-zero vector satisfying vec r*vec a=vec r*vec b=vec r*vec c=0 for given non- zero vectors vec a,vec b and vec c. statement 1:[vec a-vec bvec b-vec cvec c-vec a]=0 statement 2[vec avec bvec c]=0

For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot vec c|=| vec a|| vec b|| vec c| holds if and only if a. vec a* vec b=0, vec b* vec c=0 b. vec b* vec c=0, vec c* vec a=0 c. vec c* vec a=0, vec a* vec b=0 d. vec a* vec b=0, vec b* vec c=0, vec c* vec a=0

Let vec a,vec b,vec c be three non-zero vectors such that any two of them are non-collinear.If vec a+2vec b is collinear with vec c and vec b+3vec c is collinear with vec a then prove that vec a+2vec b+6vec c=vec 0

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

Let vec a, vec b, vec c be three non-zero vectors such that [vec with bvec c] = | vec a || vec b || vec c | then

If vec d=vec a xxvec b+vec b xxvec c+vec c xxvec a is non-zero vector and |(vec d*vec c)(vec a xxvec b)+(vec d*vec a)(vec b xxvec c)+(vec d*vec b)(vec c xxvec a)|=0 then a.|vec a|=|vec b|=|vec b|=|vec c| b.|+|vec b|+|vec c|=|d| c.vec a,vec b, and vec c are coplanar d.none of these

vec a xxvec b=vec b xxvec c!=0, where vec a,vec b, and vec c are coplanar vectors,then for some scalar k prove that vec a+vec c=kvec b

If vec A , vec B and vec C are non-zero vectors and vec A. vec B=0 and vec B. vec C=0 , then find out the value vec A .vec B

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