If `vec a, vec b, vec c` are three non collinear vectors then show that the following points are collinear. `6 vec a - 4 vec b + 10 vec c, -5 vec a + 3 vec b - 10 vec c, 4 vec a - 6 vec b - 10 vec c` and `2 vec b + 10 vec c`

If a,b, are non coplanar vectors prove that the points having the following position vectors are collinear: vec a+vec b+vec c,4vec a+3vec b,10vec a+7vec b-2vec -

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

ia,b,c are three non-coplanar vectors.Show that the points with p.v.6vec a-4vec b+10vec c,-5vec a+3vec b-10vec c,4vec a-6vec b-10vec c and 2vec b+10vec c are coplaner

If vec a,vec b,vec c are three non- null vectors such that any two of them are non-collinear.If vec a+vec b is collinear with vec c and vec b+vec c is collinear with vec a, then find vec a+vec b+vec c

If vec a , vec b , vec c are three non-zero vectors (no two of which are collinear), such that the pairs of vectors (vec a + vec b, vec c) and (vec b + vec c , vec a) are collinear, then vec a + vec b + vec c =

If vec a, vec b, vec c are three non-coplanar vectors represented by concurrent edges of a parallelopiped of volume 4, (vec a + vec b) + (vec bxx vec c) + (vec b + vec c). ( vec c xx vec a) + (vec c + vec a). (vec axx vec b) is equal to

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 and vec d are the position vectors of points A, B, C, D such that no three of them are collinear and vec a + vec c = vec b + vec d , then ABCD is a

If vec a ,\ vec b ,\ vec c are three non-zero vectors, no two f thich are collinear and the vector vec a+ vec b is collinear with vec c ,\ vec b+ vec c is collinear with vec a ,\ t h e n\ vec a+ vec b+ vec c= a. vec a b. vec b c. vec c d. none of these

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