If `a ,\ b ,\ c` are non coplanar vectors prove that the points having the following position vectors are collinear: ` vec a ,\ vec b ,\ 3 vec a-2 vec b`

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

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 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

If a ,\ b ,\ c are non zero non coplanar vectors, prove that the following vectors are coplanar. 5 vec a+6 vec b+7 vec c ,\ 7 vec a-8 vec b+9 vec c\ a n d\ 3 vec a+20 vec b+5 vec c

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

If vec a , vec ba n d vec c are non-coplanar vectors, prove that the four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+ 4 vec b-2 vec ca n d vec a-6 vec b+6 vec c are coplanar.

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

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .