Which of the following conditions are sufficient and essential for a quantity to be a vector?

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Magnitude and direction

Magnitude, direction and addition, subtraction, multiplication, and division by vector laws

Magnitude and addition, subtraction, and multiplication by ordinary rules of algebra

Magnitude, direction, and combination of vectors by ordinary rules of algebra

answer is C.

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Detailed Solution

A vector is a quantity that has both magnitude (or size) and direction. In addition, vectors must satisfy certain algebraic properties, such as the ability to be added and subtracted, multiplied by a scalar, and divided by another vector using vector laws. Therefore, option C includes all the necessary and sufficient conditions for a quantity to be considered a vector. Options A and B do not include all the necessary conditions, while option D only mentions the combination of vectors by ordinary rules of algebra, which is not sufficient to define a vector.

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