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What are the Dot products and how can you understand them?

Dot products are calculated to find the magnitude of the two vector quantities, as you are not including the direction of the vestors. The dot product is also used to find the magnitudes of the clear quantities like the area, volumes, speed, and mass. The dot product is simple multiplication of the scalar quantities but you need to use the described method as it is not like the simple multiplication. 

In the Dot product  you only need the magnitude to solve scalar quantities. no direction is required to solve the dot products. The dot product is also known as the “Scalar product” .The scalar product is equal to the magnitude of these vector quantities”. You can find the dot product of two vectors with the dot product calculator in a matter of seconds . The dot product of two vectors are perpendicular to each other. 

In this topic, we are going to identify what are the dot products and what are their applications.

How to calculate the dot products?

You calculate the various qualities by the dot product like mass, length, and time. speed. temperature etc. We find the  dot product vectors to describe how much of the force vector is used in the direction of the motion vector to find the resultant effect of the desired level.

Now the formula of the dot product is:

a.b = |a| |b| cos Q 


  • a and b are representing the the dot product 

  •  |a| & |b| describing the magnitude of the vectors

  • The perpendicular angle between the vectors Cos Q

It is quite handy to find the dot product of two  vector dot product calculator of two vector quantities.

The angle between the vectors are computed by the formula given below:

θ= Cos-1 (a.b) / |a| |b|

It is necessary to understand that the   |a| |b| representing the vectors' positive values and the modulus are making the values into the positive one.So need to consider the positive value of the magnitude of the vectors and nullify the negative values by the modulus of the dot product. The dots calculator is turning the magnitude to a positive valve of any given entry.

Example of the dot product:

Two vectors and their values are given below:

a = [-3,3,5]

b = [-4,3,5]


Step 1: 

At first Multiply the first elements of the vestors with each other

Then , (-3)*(-4) = 12

Step 2:

Now the  second element of the vectors.

Then , (3)*(3) = 9

Step 3: 

In the thyroid step multiply each vector quantity.

The , (5)*(5) = 25

Step 4:

The Dot (a.b)  product of vector = (12)+(+9)+25

 The Dot (a.b) product of vector = 12 +9 + 25

The Dot product (a.b)  of vector = 46

You can use the vector multiplication calculator to compute the dot product of two vector quantities.

The  formula or finding the dot product of the two vectors is given below:

Q= Cos-1 (a.b) / |a| |b|

Applications of dot product:

The applications of the dot product are as follows:

  • You estimate and measure by the dot product  how much of the force vector is applied in the direction of the motion vector to get the desired effect of the force.

  • The dot product is applied to the vectors which are perpendicular or parallel to each other in the coordinate plane.

  • The physical quantities are designated as the dot product or the scale qualities . These qualities are the mass, length, and time. speed.temperature etc

The dot product calculator measures the required force applied in the direction of the motion vector to get the resultant effect.


You can use the dot product to mention how closely two vectors align in terms and what is their resultant force. The solution of dot qualities of the  scalar  can be counted by the dot product. In the dot product you only need the positive magnitude of the quantities as you can’t place the sign of negative with the magnitude. The dot product identifies the force you need to apply to find the resultant effect. The dot product can be used to find the magnitude of various qualities like the mass, time, temperature etc.

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