Dot product and how you can understand it

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Dot product and how you can understand it? Dot products only need magnitude to solve scalar quantities. You need no direction to solve the dot products. The dot products are products of two scalar quantities. You may also describe them as the “Scalar product of two vectors which is equal to the magnitude of these vectors”. It is quite easy to find the dot product of two vectors with the dot product calculator.

You can say dot products are the corresponding entries of two sequences of numbers. You can find the dot products of two vectors that are perpendicular to each other. Various quantities are only solved by the dot products like mass, length, and time. speed. temperature etc. The dot product vectors describe how much of the force vector is applied in the direction of the motion vector to find the resultant effect

Dot product

In this article, we are going to discuss the formula and uses of the dot product.

How can you find dot products?

The simple formula for the scalar multiplication of two vectors is defined as “it is the multiplication of modulus of the vectors multiplied by the cos  Q”

So

a.b = |a| |b| cos Q 

Where,

  • A and b are two vectors 
  •  |a| & |b| representing the magnitude of the vectors
  • The angle between the vectors is Cos Q

You can find the dot products by the vector dot product calculator of two vector quantities.

Now the angle between the vectors can be determined by the formula given:

θ= Cos-1 (a.b) / |a| |b|

You need to understand the   |a| |b| representing the vectors’ positive values, as you will only consider the positive value of the magnitude. The dots calculator is only going to turn the magnitude to a positive valve.

Dot product  example:

Now consider two vectors and their values:

a = [-3,3,5]

b = [-4,3,5]

Solution:

Step 1 of dot products:

Multiply the first elements with each other vector

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

Step 2 of dot products:

Multiply the second element of the vectors.

Then , (3)*(3) = 9

Step 3 of dot products:

Multiply the third element of each vector quantity.

The , (5)*(5) = 25

Step 4 of dot products:

Dot products of vector = (12)+(+9)+25

Dot products of vector = 12 +9 + 25

The dot products of vector=a.b = 46

You can use the vector multiplication calculator to find the dot products of two vectors.

To determine the angle, you can find the angle by the given formula:

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

Uses of dot product:

The various uses of the dot products are as follows:

  • The dot product vectors describe how much of the force vector is applied in the direction of the motion vector to find the resultant effect. 
  • You can use the dot product measurements to find vectors that are perpendicular or parallel to each other in the coordinate plane.
  • Various physical quantities are destined as dot products. Like mass, length, and time. speed.temperature etc

The dot products calculator assists to find the required force to be applied in the direction of the motion vector to find the resultant effect.

Conclusion:

You need to use the dot products to mention how closely two vectors align in terms of their direction. You can find the solution of scalar quantities like speed, power, and time with the help of a vector dot product calculator. The dot product is usually used to find the magnitude of two scalar quantities and the angle between these quantities. You need to understand dot product is only dealing with the magnitude of the quantities, so you are dealing only with the positive number. This is the main reason we are taking the modulus of magnitude.

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