Table of Contents
What is Dot Product?
The dot product is a mathematical operation that takes two vectors and returns a single number. The number is the product of the lengths of the vectors multiplied by the cosine of the angle between them.
Concept of Dot Product
The Dot Product is a mathematical operation that takes two vectors and calculates the product of their lengths (magnitudes) and the cosine of the angle between them. The Dot Product is written as:
\begin{align}
\mathbf{A} \cdot \mathbf{B}
\end{align}
where \mathbf{A} and \mathbf{B} are vectors.
Dot Product – Geometrical Definition
The Dot Product is a mathematical operation that takes two vectors as input and produces a scalar result. The Dot Product is denoted by the symbol “·” and is defined as follows:
The Dot Product is a measure of the similarity of two vectors. The Dot Product is zero if and only if the vectors are perpendicular to each other. If the vectors are not perpendicular to each other, then the Dot Product is non-zero and is proportional to the cosine of the angle between the vectors.
Dot Product – Algebraic Definition
The dot product of two vectors is a scalar value that is the product of the lengths of the vectors multiplied by the cosine of the angle between them.
Properties of Dot Product
The dot product is a vector quantity and has the following properties:
The dot product is commutative.
The dot product is distributive.
The dot product is associative.
The dot product is symmetric.
The dot product is positive definite.
The Formula for Dot Product
The dot product is a mathematical operation that takes two vectors and calculates the product of their lengths times the cosine of the angle between them.
