Show that the vectors `2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c` are non-coplanar vectors (where ` vec a , vec b , vec c` are non-coplanar vectors)

Explanation

Given that `vec A =2 vec a- vec b+3 vec c `
`vec B =vec a+ vec b-2 vec c`
`vec C =vec a+ vec b-3 vec c`
Let `A,B,C` be points whose position vectors are `vec a,vec b,vec c`
`vec (AB)=vec a+ vec b-2 vec c-(2 vec a- vec b+3 vec c)`
`=- vec a+2 vec b - 5 vec c `
`vec(BC)=vec a+ vec b-3 vec c-(vec a+ vec b-2 vec c)`
`=- vec c `
hence `vecA,vec B,vecC` are non-coplanar vectors