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The dot product is a mathematical tool used for handling vectors. To calculate the dot product of two vectors, first put the vectors together and find the angle between them. The dot product is the magnitude of vector A times the magnitude of vector B times the cosine of the angle between them, representing the projection of one vector onto the other. This results in a scalar quantity. The terms "dot product" and "scalar product" are used interchangeably. When finding the dot product of a vector with itself, the result is the square of the magnitude of the vector.