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`

Explanation

We are given the vectors


`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`


Now to show non-coplanar of the vectors we must satisfy the condition

`[ vec(A) quad vec(B) quad vec(C)] != 0`


`rArr |[2,-1,3],[1,1,-2],[1,1,-3]|`


`=2[(1)(-3)-(1)(-2)]-(-1)[(1)(-3)-(1)(-2)]+(3)[(1)(1)-(1)(1)]`


...