Show that the points `A ,B ,C` with position vectors `-2 vec a+3 vec b+5 vec c , vec a+2 vec b+3 vec ca n d7 vec a- vec c` respectively, are collinear.

Explanation

Let `A,B,C` be points whose position vectors are `vec a,vec b,vec c`
`vec (AB)= vec a+2 vec b+3 vec c-(-2 vec a+3 vec b+5 vec c)`
`=3 vec a- vec b-2 vec c`
`vec (BC) =7 vec a- vec c-(vec a+2 vec b+3 vec c)`
`=6 vec a-2 vec b - 4 vec c`
clearly from above, we can conclude ,
`vec(BC)=2vec (AB)`b