It depends on how they are defined and since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
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There are binary vectors in computer technology and in genetics. The two are entirely different and the question needs to be more specific.
Cross product is a mathematics term when there is a binary operation on two vectors in three-dimensional space.
Yes it is :)
False
in mathematics the cross products are the binary operation on two vectors in a 3dimensional Euclidean space that results in another vector which is perpendicular to the containing the 2 inputs vector.