Articles containing proofs | Tensors | Scalars | Bilinear forms | Operations on vectors | Analytic geometry
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). 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 between two vectors is the quotient of their dot product by the product of their lengths). 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. (Wikipedia).
Introduction to the Dot Product
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From playlist Calculus 3
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Proof of the Dot Product Theorem
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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is dot product or scalar product of 2 vectors A and B. Then I will give 4 “typical” examples of dot products. Next video in the series can be seen at: https://youtu.be/Q3FVhpsF5aU
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
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Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! ►PRODUCT RECOMMENDATIONS https://www.amazon.com/shop/brithem
From playlist Calc 3
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From playlist Introduction to Vectors
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Part III: Linear Algebra, Lec 7: Dot Products
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