Why do you Need the Dot Product of Two Vectors?

⁡You can solve the dot products to solve scalar quantities, for the scalar quantities only need the magnitude of the two quantities. Consider if a force is applied at an angle θ to the displacement, then the work done can be measured by the dot product formula = θ W = f d cos. The dot products are equal to the cross product of the magnitude of two vectors. You only need the positive values of the magnitude, and therefore for finding the dot products.

You need to use the modulus of the two vector quantities, when you are taking the modulus, then only positive values are going to be used. The dot product calculator is handy to find the dot product of two vector quantities. The dot product of a vector measures how much of the force is going to be used in the direction of motion to find the resultant product.

In this article, we are discussing what are the dot products and how you can find them.

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The Method of Solving Dot Product

The formula for measuring the scalar multiplication of two vectors is: 

a.b = |a| |b| cos Q 

Here

• a and b are two vectors 
• |a| & |b| positive values of vectors
• cos Q  is the angle between the vectors is Cos Q

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

The vectors can be determined by the formula given:

θ= Cos-1 (a.b) / |a| |b|

The angle between the two vectors is the inverse of the cos θ and you can use the vector dot product calculator to find the angle

Example of Dot Products

Consider a vector “a = [-5,3,5]” and “b = [-4,3,5]”

Now consider two vectors and their values:

a = [-5,3,5]
b = [-4,3,5]

Solution:

The first step of dot product:

Multiply (-5) and (-4) with each other vector

Then , (-5)*(-4) = 20

The second step of dot product:

Multiply (3) and (3) the second element of the vectors.

Then , (3)*(3) = 9

The third step of dot product:

Multiply (5) and (5) the third element of each vector quantity.

The , (5)*(5) = 25

The fourth step of dot product:

Dot product of vector of two vectors = (20)+(+9)+25

The dot product of the vector of two vectors= 20 +9 + 25

The dot product of the vector of two vectors = a.b = 54

The vector multiplication calculator is going to find the dot product of two vector quantities.

How to find the angle of the dot product?

The angle of the dot product is the Cos-1[a.b/|a| |b|], of vectors.  

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

The dot product calculator is used to find the angle between the two vectors.

The Applications of the Dot Products

We use the dot product in the field of physics and mathematics:

• You can estimate the resultant force required for moving the object in the desired direction by the dot product estimation.
• Find the vectors that are perpendicular or parallel to the coordinate plane.
• You can measure various dot product quantities by the dot product like mass, time, speed, etc.

The dot product calculator helps to find the required force in the direction of the motion vector to find the resultant effect.

Conclusion

You can estimate how closely two vectors align in their direction. You can find the resultant force by the dot product calculator. You can measure the angle of the dot product of two scalar quantities by the dot product along with their angle. You need to understand dot product is a basic measurement when dealing with scalar quantities. 

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