Using cross product to determine if vectors are parallel

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The discussion clarifies that when the cross product of two vectors u and v equals zero, it indicates that the vectors are parallel. The zero result refers specifically to the zero vector, represented as (0,0,0). This outcome occurs because the cross product measures the area of the parallelogram formed by the vectors, which is zero when they are parallel. Understanding this concept is crucial for applying vector mathematics correctly. The clarification emphasizes the significance of the zero vector in the context of vector operations.
aero_zeppelin
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My question is simple:

I understand that if u x v = 0 , then u and v are parallel, but what does that 0 mean?
You can't obtain 0 by crossing two vectors. By 0, does it mean (0,0,0)?
 
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Yes, it means the zero vector, (0,0,0) .
 
thanks! ;)
 

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