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# What Are Vectors in Precalculus?

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A vector is a mathematical entity that has both magnitude and direction or is an element of a vector space. A vector is typically represented graphically by an arrow with its tip indicating the direction, while its length represents its magnitude. By denoting the origin end of the arrow with the letter O and the tip with the letter A, the vector can be represented algebraically as vector OA.

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Credit: lambada Digital Vision Vectors Getty Images

If two vectors have similar magnitude and direction, they are considered as equal, no matter what their points of origin are. However, vectors that have equal magnitude but opposite direction are not the same and are equated to each other with a negation sign. The addition of vectors involves the placement of the origin of the second vector on the tip of the first vector followed by the drawing of a line starting at the origin of the first vector and ending at the tip of the second vector. The subtraction of vectors operates in the opposite direction where the second vector is negated then placed on the tip of the first vector. Other laws of ordinary algebra, such as the commutative laws for addition and multiplication and the distributive law, are applicable to vectors.