Show that points with position vectors `2-2b+3c,-2a+3b-c and 4a-7b+7c` are collinear. It is given that vectors a,b and c and non-coplanar.

Explanation

The three points are collinear, if we can find `lamda_(1),lamda_(2) and lamda_(3),` such that
`lamda_(1)(a-2b+3c)+lamda_(2)(-2a+3b-c)+lamda_(3)`
`(4a-7b+7c)=0` with `lamda_(1)+lamda_(2)+lamda_(3)=0`
On equating the coefficient a,b and c separately to zero, we get
`lamda_(1)-2lamda_(2)+4lamda_(3)=0,-2lamda_(1)+3lamda_(2)-7lamda_(3)=0` and
`3lamda_(1)-lamda_(2)+7lamda_(3)=0`
On solving we get `lamda_(1)=-2,lamda_(2)=1,lamda_(3)=1`
so that, `lamda_(1)+lamda_(2)+lamda_(3)=0`
hence, the given vectors are collinear.