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Can different vectors have the same components?

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It is obvious that an infinite number of vectors can have the same components [3,4], since there are an infinite number of pairs of points in the plane with x - and y -coordinates whose respective differences are 3 and 4. All these vectors have the same magnitude and direction, being parallel to one another, and are considered equal. Thus, any vector with components a and b can be considered as equal to the vector [ a,b ] directed from the origin (0,0) to the point ( a,b ). The concept of a vector can be extended to three or more dimensions.

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