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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.
Learn how to calculate the dot product of two vectors using different methods and formulas. The dot product gives a scalar (number) that depends on the length and angle of the vectors.
Dot Product of vectors is equal to the product of the magnitudes of the two vectors, and the cosine of the angle between the two vectors. The dot product of two vectors a and b is given by a ⋅ b = |a| |b| cos θ.
Sep 7, 2022 · The dot product essentially tells us how much of the force vector is applied in the direction of the motion vector. The dot product can also help us measure the angle formed by a pair of vectors and the position of a vector relative to the coordinate axes. It even provides a simple test to determine whether two vectors meet at a right angle.
Algebraically, the dot product is defined as the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the two vectors’ Euclidean magnitudes and the cosine of the angle between them.
Learn how to calculate the dot product of two vectors, which measures how much they point in the same direction. See the intuition behind the formula, the law of cosines, and some applications in physics.
The dot product of the vectors a a (in blue) and b b (in green), when divided by the magnitude of b b, is the projection of a a onto b b. This projection is illustrated by the red line segment from the tail of b b to the projection of the head of a a on b b.
