There are binary vectors in computer technology and in genetics. The two are entirely different and the question needs to be more specific.
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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.
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
Resultant vector or effective vector
Vector spaces can be formed of vector subspaces.