Define the work of a vector
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work is the amount of energy required to perform a given task (such as moving an object from one point to another). We start by defining the scalar product of two vectors, which is an integral part of the definition of work, and then turn to defining and using the concept of work to solve problems.
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A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. Two examples of vectors are those that represent force and velocity.
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