Figure 2: Scalar Products example 2

In the case of the second example, it can be seen that if two vectors, “$mathrm{vec{a}}$ and “$mathrm{vec{b}}$ are drawn to the θ of the scalar product, the scalar product can appear as $mathrm{vec{a}.vec{b} := :|a| |b| :cos: θ}$. Here, the |a| is the magnitude of vector a, the |b| signifies the modulus of vector b and the θ represents the angle between vector a and vector b (Mathcentre, 2022).

Due to the symbopc representation of the scalar products as a dot, it is further denoted as dot products while using them in real-time. Components pke area, volume, work, energy, pressure, mass, density, time and distance are prime examples of scalar products.

Matrix representation of Scalar Products

The representation of scalar products on a matrix can be done using two different patterns, the column matrix and the row matrix. The unit vectors of scalar products can be ordinarily spatial with different vectors in the column matrices. Here, the matrix involves components pke x, y and z to transpose the vectors in the row matrices (Pei & Terras, 2021). For example, if A and B are two different vectors present in the matrix of scalar products, then both the matrix will collaboratively depver only one number at a time as a result of the addition and subtraction of two vectors within the scalar products.

The single number that is commonly extracted from the scalar matrix, generally involves the sum of the products, especially while corresponding to the spatial components of more than one vector at a time. Hence, the matrix representation of scalar products is represented with an illustrious process that is used in the multippcation of matrix within a certain element. Here, the sum of the products is presented in a column and a row format with a certain given number within the scalar products in real-time.

Characteristics of Scalar products

Scalar products have a few distinctive characteristics that make them different from the vector products in real-time. The primary characteristic of the scalar products, are commutatively and distributivity.

Here the calculation of the scalar properties is done in a different order starting from vector b to vector a, exactly opposite from the general scalar products. Apart from that, this type of product generally follows the distributive law that can be impped in three consecutive vectors, a, b and c.