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`

Explanation

Given: `vec(a), vec(b), vec(c)` are non-coplanar vectors.


Let the points be with the position vectors


`A= vec(a)`


`B= vec(b)`


`C= 3 vec(a)-2 vec(b)`


Then `vec(A B)=` Position vector of `B-` Position vector of `A`


`=vec b- vec a`


`rArr vec(AB)=- vec(a)+ vec(b)`


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