Dot Product Calculator
Vector multiplication is a common task that needs to be done by Mathematics as well as Physics students. Mainly, this product can be carried out through two main methods that are dot product and cross product. The dot product is rather simple than the cross product but it can be still difficult for students.
If you also find it hard, you can use a dot product calculator that will seamlessly give you results after the multiplication of the given vectors. This maths calculator will not ask you to follow different steps for completing this task. But you can find the dot product just by inserting the coordinates of the vector in the mentioned boxes. Want to know about this tool more? Keep reading!
Table of Contents
What is Dot Product?
The dot product (also called the Scalar product) is the production of scalar components of two or more vectors. It means that the numbers showing the coordinates will be multiplied only. The term that will come out as the resultant won’t have any directional/unit vector.
That’s why it is also called a Scalar product because the result is a scalar quantity. To show the dot product between two products, we need to put a heavy dot between the vectors. For example, if we have two vectors A and B, we will write their dot product as “A . B”
What is a dot product of vectors?
The dot product of vectors is the scalar product of those vectors that will result in a scalar quantity. It means that we will get a number as the final result that won’t have any direction. The dot product of two parallel vectors will always be 1 while the dot product of two perpendicular vectors will be 0.
That’s why, the parallel components while multiplying with each other gives 1 as the resultant while when perpendicular components are multiplied, the resultant will be 0. On the other side, there is another type of product of vectors that we call cross-product.In cross-product, the product between parallel and perpendicular vectors will be reversed as compared to the dot product with vectors.
Dot product formula
Vector product has a particular formula that you need to follow for finding the resultant. Here is the formula that you need to follow for the dot product of two vectors.
A . B = A B cos θ
On the right side of the equation,
- A and B are the scalar values of the given vectors
- “θ” is the angle between these vectors
How to calculate dot product?
As discussed earlier, we have to multiply the coefficients of the same coordinates of the vectors to find the dot product. To let you understand the procedure, we have solved an example here.
Example 1:
Find the dot product of two parallel vectors given below:
A = 3i -2j +3k
B = 2i -7j + 12k
Solution:
As we know that we have to multiply the components with the same unit vectors. Also, the angle between two parallel vectors is “0”. So,
A . B = (3 x 2) + (-2 x -7) + (3 x 12) cos0
We also know that cos0 = 1. So,
= 6 -14 +36
= 28
How to use the dot product calculator?
If you have complex values to deal with and are unable to find the dot product of two vectors, you can use this calculator by Calculator’s Bag. This tool can find the answer to the dot product of two vectors with any components within seconds. Follow these steps to use this tool for dot product calculation.
- Insert the components of the first vector
- Insert the components of the second vector
- This calculator will automatically show the final answer of the product
FAQ | Dot Product
What are the rules for a dot product?
To find the dot product of two vectors, you have to multiply the components of the same unit vector. It means you have to multiply the component of “i” of the first vector with the component of “i” of the second vector and so on for other vectors.
What does the dot product depend on?
The dot product depends on the angle between the given vectors.
Why do we need a dot product?
The dot product shows the position of the resultant of the given vectors that estimate many other aspects related to vectors.
What happens if the dot product is greater than 0?
It shows that the two vectors are pointing in the same direction which means that the vectors are parallel.
Why is dot product important in mechanics?
The dot product gives an estimation of the force vector that is useful in different fields of mechanics.
What is the dot product of two unit vectors?
The dot product of two same unit vectors will be 1 while the dot product of two perpendicular unit vectors will be 0.
