Multiplication Two Vectors Definition, Use, Facts & Examples

Is this page helpful?

About Dot Product

The dot product is one of the methods of multiplication of two vectors. A scalar quantity is the outcome of the dot product of vectors. As a result, the dot product is also referred to as a scalar product. It is the geometric product of the Euclidean magnitude of two vectors and the cosine of their angle. In geometry, mechanics, engineering, and astronomy, the dot product of vectors has several uses. We'll go through the dot product in further depth in the following sections.

The dot product of two vectors

The product of magnitudes of two vectors and the cosine of the angle between them is known as the dot product of the vectors. The dot product of two vectors produces a resultant in the same plane as the two vectors. The dot product can be either a positive or negative real value and is scalar in nature. Do check out more Maths Formulas.

Dot product definition

Let the two vectors: a= [a₁,a₂,a₃,a₄,….,a_n] and b = [b₁,b₂,b₃,b₄,….,b_n]

then their dot product is:

a.b = a₁b₁+a₂b₂+a₃b₃+……….a_nb_n

$\underset{a}{\to} . \underset{b}{\to} = \sum_{i = 1}^{n} a_{i} b_{i}$

Dot product formula

Let a and b be the two non-zero vectors, and θ is the angle between the vectors. Then the dot product or scalar product is denoted by a.b, which is defined as:

$\underset{a}{\to} . \underset{b}{\to} = |\underset{a}{\to}| |\underset{b}{\to}| \cos θ$

Here,

$|\underset{a}{\to}|$ Is the magnitude of $\underset{a}{\to}$

$|\underset{b}{\to}|$ is the magnitude of $\underset{b}{\to}$ and θ is the angle between them.

Dot product

Geometrical meaning of dot product

The dot product of two vectors is made by multiplying the component of one vector in the direction of the other by the magnitude of the other vector. To comprehend the vector dot product, we must first learn how to calculate the magnitude of two vectors and the angle between two vectors to calculate one vector's projection over another.

Dot product

About Dot Product

The dot product of two vectors

Dot product definition

Dot product formula

Download The pdf of Dot Product

NCERT Solutions All Classes