Dot Product Calculator
Calculate mathematical dot products, scalar products and dot product angles easily for your vectors.
Table of contents
About scalar product calculator
Finding out the dot product of vectors can be challenging. With this page, you can calculate dot products easily, and find all the essential information about dot products that you need to know.
How to use dot product calculator?
Add your vector coordinates to the dot product calculator, and you get a scalar result.
If you have 2-dimensional coordinates, add 0s' to z-coordinates and you can use the calculator for your vectors.
What is a dot product?
The dot product is a way to multiply vectors that result in scalar quantity. The dot product is also often referred to as a scalar product. The result of the dot product is dependent on the angle between the vectors and the lengths of the input.
Dot product in math
Therefore dot product is a simple but fundamental concept that converts similarities between different vectors into a scalar result.
What is the formula of dot product?
The dot product of two vectors that are defined as a and b are following:
a⋅b = |a| * |b| * cosθ
What is the formula of dot product angle?
The dot product angle formula for two vectors that are defined as a and b is following:
cosθ = a·b / (|a| * |b|)
How to calculate dot product?
The dot product between vectors is computed by estimating how many vectors are pointing in the same direction as one another.
Dot product calculation is simply done by multiplying vectors' respective coordinates and adding them up.
For two vectors a and b, dot product is calculated as following:
(a1 * b1) + (a2 * b2) + (a3 * b3) .... + (an * bn)
What is the difference between positive and negative dot products?
The quantity that gets given is relative to the two vectors' directions.
If the angle between them is lesser than 90 degrees, the dot product will be positive, and they are closer to being in similar directions.
Positive and negative dot product
If the angle between them is greater than 90 degrees, the dot product will be negative, and they are closer to being in opposite directions.
What happens when a dot product is 0?
If the two sides are perpendicular to each other at 90 degrees, the dot product is zero.
What is the difference between dot product and cross product?
The dot product of two vectors shows the magnitude of the two vectors and the cosine of the angle that they form with each other.
A cross product of two vectors is produced by the sine of angle that they form with each other and the magnitude of the two vectors.
The difference between a dot product and a cross product is that the former is a scalar quantity, while the latter is a vector quantity.
Therefore the result of the dot product is a single number and the result of the cross product is a vector.
How to calculate matrix dot product?
To get the matrix dot product, the rows of the first matrices and columns of the second matrices have to have the same length.
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.
Dot Product Calculator English
Published: Tue Aug 24 2021
Latest update: Mon Oct 18 2021
In category Mathematical calculators
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