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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 and often called "the" inner product (or rarely projection product) of Euclidean space even though it is not t...


Although this formula is nice for understanding the properties of the dot product, a formula for the dot product in terms of vector components would make it easier to calculate the dot product between two given vectors.


Since the projection of a vector on to itself leaves its magnitude unchanged, the dot product of any vector with itself is the square of that vector's magnitude. A · A = AA cos 0° = A 2. Applying this corollary to the unit vectors means that the dot product of any unit vector with itself is one.


A formula for the dot product is as follows: [math]\vec{A} \cdot \vec{B} = \lvert \vec{A} \rvert \lvert \vec{B} \rvert \cos(\theta)[/math] Where [math]\theta[/math ...


Calculating the dot and cross products when vectors are presented in their x, y, and z (or i, j, and k) components. ... Calculating dot and cross products with unit vector notation. This is the currently selected item. ... Calculating dot and cross products with unit vector notation.


Calculation of Unit Vector Dot Product. All unit vectors have magnitude 1 and the unit vectors in a three dimensional coordinate plane, that is, the unit vectors `hati` , `hatj` and `hatk` , are perpendicular to each othe. Thus, the angle between two unit vectors is `theta` = 90 degrees. Thus, the resultant of the dot products of unit vectors can be predetermined.


The dot product of two parallel vectors is equal to the algebraic multiplication of the magnitudes of both vectors. If the two vectors are in the same direction, then the dot product is positive. If they are in the opposite direction, then the dot product is negative.


Dot Product A vector has magnitude (how long it is) and direction:. Here are two vectors: They can be multiplied using the "Dot Product" (also see Cross Product).. Calculating. The Dot Product gives a number as an answer (a "scalar", not a vector).. The Dot Product is written using a central dot: a · b This means the Dot Product of a and b . We can calculate the Dot Product of ...


Range of the Dot Product of Two Unit Vectors. Here is a sampling of b u and the dot product with a u = (1.0, 0) T for various angles.


Vectors - Dot Product - Vectors Dot Product - Vectors and Calculus Video Class - Vectors and Calculus Video Class for IIT JEE exams preparation and to help CBSE, Intermediate students covering Introduction to Physical Quantities, Terminologies and General Properties, Addition of Vectors Triangle Law, Parallelogram Law, Formula, Subtraction of Vectors, Subtraction formula, Resolution of Vectors ...