Dot Product Calculator

Formula

The formula to calculate the dot product between two equal-length vectors is:

\[ \text{Dot Product} = \sum_{i=1}^{n} a_i \cdot b_i \]

Where:

\( n \) is the total number of components in the vectors
\( a \) and \( b \) are vectors of equal length
\( a_i \) and \( b_i \) are the components of vectors \( a \) and \( b \) respectively

What is Dot Product?

A dot product, also known as a scalar product, is an algebraic operation between two sequences of numbers that returns a single number. In most cases, these sequences are represented by vectors. The dot product is calculated by multiplying corresponding components of the vectors and then summing these products.

Example Calculation

Let's assume the following vectors:

Vector A: 2, 3, 4
Vector B: 1, 0, 1

Step 1: Calculate the Dot Product:

\[ \text{Dot Product} = (2 \cdot 1) + (3 \cdot 0) + (4 \cdot 1) = 2 + 0 + 4 = 6 \]

Therefore, the dot product is 6.