Answer to Question #262735 in Analytic Geometry for Almas

Question

Definition, Formula and Physical interpretation of Dot Product

Answer 1

Solution:

The dot product, also called the scalar product, of two vector s is a number ( Scalar quantity) obtained by performing a specific operation on the vector components. The dot product has meaning only for pairs of vectors having the same number of dimensions. The symbol for dot product is a heavy dot ($\cdot$ ).

Formula:

$a \cdot b=\sum_{i=1}^{n} a_{i} b_{i}$

a=1st vector

b=2nd vector

n=dimension of the vector space

a_i=component of vector a

b_i=component of vector b

Physical interpretition:

The dot product of two vectors gives a scalar, that means only the magnitude is left, no direction.

Mathematically, it is equal to the product of the magnitude of two vectors times the cosine of the angle between the two.

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.