Vector A
Vector B
Dot Product

​Dot Product

The Dot product is the result of multiplying two vector quantities. It is often known as a scalar product. This emphasizes the magnitude of the value only. The word scaler predicts that the answer will be scaler quantity rather than vector quantity. However, it deals with the single dimension of the value, rather than the three-dimensional value.

 

Formula of ​Dot Product Calculator

The dot product is represented by a dot between two values. i.e

A.B = |A| |B| cos(θ)

Where,

|A| = magnitude of the vector quantity A

|B| = magnitude of the vector quantity “B”

θ (theta) = angle between A and B

Note:

To gain knowledge about the cross product, click the Cross Product Calculator.

Properties of Dot Product

The characteristics of dot products are as follow:

Distributive Quantity

The value outside the bracket is multiplied by both terms inside i.e.,

A . ( B + c ) = A . B + B . C

Commutative

Multiplying the values in either order will have the same result. i.e.,

A . B = B . A

Bilinear

The results of combining elements of two vector values in either pattern will be the same. i.e.,

A(RB + C) = R(A . B) + (A . C)

Scalar Multiplication

In scalar multiplication, you can take the common values inside the bracket. i.e.,

(C1A) . (C2B) = C1C2 (A . B)

Example

Calculate the dot product of vectors A and B, where A = 8, B = 15, θ = 60°.

Given data

A = 8
B = 15
θ = 60°

To Find

A.B = ?

Solution

As we know,

A.B = |A| |B| cos(θ)

Putting values in the formula:

A.B = (8) (15) cos(60)
A.B = (120) (0.5)
A.B = 60

Therefore, the dot product of vectors A and B is A.B = 60

How to use ​Dot Product Calculator?

The steps to use ​the dot product calculator are as follows:

Step 1: Enter the values of vector A in the first required input.

Step 2: Enter the values of vector B in the second required input.

Step 3: The calculator will automatically display an answer on the screen.

Calculator use

What function does a dot product calculator perform? You just have to put values for the components of each vector and click on the button below. After a few seconds results will appear on your screen. It automatically generates the answer to your problems. You can solve even complex questions using calculatorsbag's calculators. For an advanced-level question, add more than a single value and you will get the solution along with the final answer. You can add negative values, fractions, mixed numbers, and rational numbers to create your question.