Question about cross product of 2 vectors, need help!

Question

If the cross product of $2$ vectors is the surface they clamp. if you let one vector go against zero, shouldn't be cross product then be the lenght of the other one? I'm hoping for explanation. I mean if you let one vector go against an infinite small amount towards zero, the cross product should be the lenght of the other vector.

Answer 1

No it is not, note indeed that more in general

$$|S|=|A\times B|$$

but

$$|A\times 0|=0$$

(credit Wikipedia)

Answer 2

No: when you shrink one vector to zero, the parallelogram becomes infinitely thin, and thus its area goes to zero as well.