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Dot product - Wikipedia
https://en.wikipedia.org/wiki/Dot_product
WEBIn 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.
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Dot Product - Math is Fun
https://www.mathsisfun.com/algebra/vectors-dot-product.html
WEBThe dot product of two vectors that point in the same direction is the simple product of their lengths, because the angle is 0 degrees which has a cosine of 1. a · b = |a| × |b| × cos(0°) a · b = a × b × 1. a · b = ab. Right-Angled Triangle. Let's use the dot product on a right-angled triangle!
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Dot products (article) | Khan Academy
https://www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function/x786f2022:vectors-and-matrices/a/dot-products-mvc
WEBThe units for the dot product of two vectors is the product of the common unit used for all components of the first vector, and the common unit used for all components of the second vector. For example, the dot product of a force vector with the common unit Newtons for all components, and a displacement vector with the common unit meters for ...
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Dot Product - Formula, Examples | Dot Product of Two Vectors
https://www.cuemath.com/algebra/dot-product/
WEBDot Product Definition. In vector algebra, if two vectors are given as: → a a → = [ a1 a 1, a2 a 2, a3 a 3, a4 a 4 ,…., an a n] and → b b → = [ b1 b 1, b2 b 2, b3 b 3, b4 b 4 ,…., bn b n] then their dot product is given by: → a ⋅ → b a → ⋅ b → = a1b1 a 1 b 1 + a2b2 a 2 b 2 + a3b3 a 3 b 3 +……….+ anbn a n b n.
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4.7: The Dot Product - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)/04%3A_R/4.07%3A_The_Dot_Product
WEBSep 17, 2022 · In words, the dot product of two vectors equals the product of the magnitude (or length) of the two vectors multiplied by the cosine of the included angle. Note this gives a geometric description of the dot product which does not depend explicitly on the coordinates of the vectors.
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12.3: The Dot Product - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/12%3A_Vectors_in_Space/12.03%3A_The_Dot_Product
WEBSep 7, 2022 · Definition: dot product. The dot product of vectors ⇀ u = u1, u2, u3 and ⇀ v = v1, v2, v3 is given by the sum of the products of the components. ⇀ u ⋅ ⇀ v = u1v1 + u2v2 + u3v3. Note that if u and v are two-dimensional vectors, we calculate the dot product in a similar fashion.
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Dot Product | Brilliant Math & Science Wiki
https://brilliant.org/wiki/dot-product-definition/
WEBThe specific case of the inner product in Euclidean space, the dot product gives the product of the magnitude of two vectors and the cosine of the angle between them. Along with the cross product, the dot product is one of …
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Dot Product -- from Wolfram MathWorld
https://mathworld.wolfram.com/DotProduct.html
WEB4 days ago · From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/DotProduct.html. The dot product can be defined for two vectors X and Y by X·Y=|X||Y|costheta, (1) where theta is the angle between the vectors and |X| is the norm. It follows immediately that X·Y=0 if X is perpendicular to Y.
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10.3: The Dot Product - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/10%3A_Vectors/10.03%3A_The_Dot_Product
WEBDec 29, 2020 · The dot product of \(\vec u\) and \(\vec v\), denoted \(\vec u \cdot \vec v\), is \[\vec u \cdot \vec v = u_1v_1+u_2v_2+u_3v_3.\] Note how this product of vectors returns a scalar , not another vector.
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Dot product - Math.net
https://www.math.net/dot-product
WEBIf v = [ v1, ... , vn] T and v = [ w1, ... , wn] T are n -dimensional vectors, the dot product of v and w, denoted v ∙ w, is a special number defined by the formula: v ∙ w = [ v1w1 + ... + vnwn] For example, the dot product of v = [ -1, 3, 2] T with w = [ 5, 1, -2] T is: v ∙ w = ( -1 × 5) + ( 3 × 1) + ( 2 × -2) = -6.
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