Convex Combination for two points(2 coordinate or three coordinate).
The convex combination for any two points p,q in a plane is α1p+α2q with α1+α2=1.
In example 1 the sum of alpha 1 and alpha 2 are not equal to 1 as per rule. But when alpha values are provided in hand you can use it as such without any checking. α1+α2=1 rule can be applied to find the solution of alpha 2 when only alpha 1 is provided. alpha values are assumptions on deviations.