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Given two vectors
they are parallel if they are a multiple of each other:
You can easily test this by checking if
they are orthogonal if their dot product is null:
For example, in the first case, we have
So, they aren't parallel. Similarly, you have
So, they aren't orthogonal.
In the second case, we have
So, they aren't parallel, and
So, they are orthogonal.
Finally, we have
So, they are parallel (and thus can't be orthogonal)