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 ca n d vec b+ vec c` is collinear with ` vec a ,` then find ` vec a+ vec b+ vecc`

Let vec a , vec b, vec c be three non-zero vectors such that any two of them are non-collinear. If vec a+2 vec b is collinear with vec ca n d vec b+3 vec c is collinear with vec a then prove that vec a+2 vec b+6 vec c= vec0

If vec a , vec b and vec c are three non-zero vectors, no two of which are collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c| .

If vec a ,\ vec b ,\ vec c are three non-zero vectors, no two of which 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= vec a b. vec b c. vec c d. none of these

Given three vectors vec a , vec b ,a n d vec c two of which are non-collinear. Further if ( vec a+ vec b) is collinear with vec c ,( vec b+ vec c) is collinear with vec a ,| vec a|=| vec b|=| vec c|=sqrt(2)dot Find the value of vec a. vec b+ vec b. vec c+ vec c. vec a a. 3 b. -3 c. 0 d. cannot be evaluated

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 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 non coplanar vectors, prove that the following vectors are non coplanar: \ 2 vec a- vec b+3 vec c ,\ vec a+ vec b-2 vec c\ a n d\ vec a+ vec b-3 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 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 non coplanar vectors, prove that the following vectors are non coplanar: \ vec a+2 vec b+3 vec c ,\ 2 vec a+ vec b+3 vec c\ a n d\ vec a+ vec b+ vec c