What is a vector?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A vector is an entity that requires two features to be defined: magnitude and direction. Unlike scalar quantities that only require a magnitude to be completely defined, vectors need a direction in which they act in addition to the magnitude of the quantity that is acting in that direction.

Some examples of quantites that need vectors for them to be defined are displacement, velocity, acceleratio, force, etc. Quantities like distance, speed, etc. are scalar in nature.

As an example differentiating vectors and scalars consider two points A and B. The separation between the points is a scalar quantity called distance. The movement of an object from A to B or from B to A is represented by a vector quantity called displacement. Displacement has a magnitude that is equal to the distance between A and B. In addition displacement also has a direction that differentiates a movement from A to B from that of a movement from B to A.

`vec (AB) != vec (BA)` , instead `vec(AB) = -vec(BA)` .