what does the word product mean in math
Product (mathematics) In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. Thus, for instance, 6 is the product of 2 and 3 (the result of multiplication), and   x ⋅ ( 2 + x )  {\displaystyle x\cdot (2+x)}  is the product of   x  {\displaystyle x}  and   ( 2 + x )  {\displaystyle (2+x)}  (indicating that the two factors should be multiplied together).
Multiplication The numbers to be multiplied are generally called the "factors". The number to be multiplied is called the "multiplicand", while the number of times the multiplicand is to be multiplied comes from the "multiplier". Usually the multiplier is placed first and the multiplicand is placed second,[1] however sometimes the first factor is the multiplicand and the second the multiplier.[6] Additionally, there are some sources in which the term "multiplicand" is regarded as a synonym for "factor".[7] In algebra, a number that is the multiplier of a variable or expression (e.g., the 3 in 3xy2) is called a coefficient.
Dot product Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In modern geometry, Euclidean spaces are often defined by using vector spaces. In this case, the dot product is used for defining lengths (the length of a vector is the square root of the dot product of the vector by itself) and angles (the cosine of the angle of two vectors is the quotient of their dot product by the product of their lengths).
Dot product The name "dot product" is derived from the centered dot " · " that is often used to designate this operation; the alternative name "scalar product" emphasizes that the result is a scalar, rather than a vector, as is the case for the vector product in three-dimensional space.