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We say that a point C (anywhere) on an axis that contains a vector AB ≠...

We say that a point C (anywhere) on an axis that contains a vector AB ≠ 0 ( and so A ≠ B), divides the vector AB ≠ 0 in ratio λ, if (AC/CB) = λ . This ratio is also called the simple ratio of the points A, B, C in the order denoted by {A, B; C}. So, when A ≠ B prove:

(a) C is between A and B iff λ > 0.

(b) C is outside A and B iff λ < 0.

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