How to determine the right or left triple (vectors)?

Question

Geometry

The textbook provides examples of parallelepipeds built as written on the left and right three.
But I can not understand why the triplets are different, if in both cases the direction is counterclockwise.
Can you please tell me why there is a left three in the second picture?

Answer 1

On the left picture a->b->c is clockwise, on the right a->b->c is counterclockwise

Answer 2

The question is old, but if someone has more developed spatial-figurative thinking, then there is one mnemonic. We were told at the institute that you can determine by the hand. You make a "basis" of the fingers: palm towards you, the first vector - thumb up, the second vector - the index finger to the side, the third vector - the middle finger towards you. Then we look at which hand is more suitable. If it turns out to "substitute" the right hand without changing the continuation of the fingers (this is important), then the triple is right. The counter-clockwise rule also applies.