Dot Product Calculator
Free Dot Product Calculator tool determines the dot product of two or more vectors quickly. To obtain the dot product value give the vector components as inputs and press the calculate button.
Dot Vector Calculator: Do you want to calculate the dot product of vectors? If yes, then utilise this handy tool. You can get the detailed step-by-step process to compute the vectors dot product and solved examples here. Also, get the complete details about the concept dot product in the following sections.
What is Dot Product?
The dot product is the scalar product. It is the scalar quantity which is obtained from the specific
operations
on the vector components. The dot product of vectors is represented using a dot. The dot is used to
check
whether two vectors are orthogonal or not.
In short terms, the dot product is the result of
multiplying the
numerical values in 2 or more vectors. If a is an vector with values (a1, a2,
a3, . . an) and b is an vector with values (b1, b2, b3, .
.
bn)
The dot product is a . b = (a1 * b1) + (a2 * b2) + (a3 * b3). . + (an * bn)
The general dot product formula is a . b = (a1 * b1) + (a2 * b2) + (a3 * b3)
Another dot product formula is a · b = |a| × |b| × cos(θ)
How to Find Dot Product of Vectors?
The simple step-by-step process to calculate the dot product of two or more vectors is along the lines:
- Get the individual values of the vectors.
- Multiply the corresponding values from every vector.
- Then, add them to obtain the dot product value.
Example:
Find a . b when a = (3, 5, 6) and b = (2, 7, 10)
Solution:
Given vectors are a = (3, 5, 6) and b = (2, 7, 10)
Dot product of vectors is a . b = (a1 * b1) + (a2 * b2) + (a3 * b3)
= (3 * 2) + (5 * 7) + (6 * 10)
= 6 + 35 + 60
= 101
FAQ's on Dot Product Calculator
1. Can you multiply dot product?
Yes, the multiplication of two or more vectors is the dot product.
2. What is the dot product of two numbers?
The dot product is the sum of the products of the corresponding values of two numbers.
3. What is the purpose of the dot product?
The dot product tells us how much of the force vector is applied in the direction of the motion vector. It is helpful to measure the angle formed by a pair of vectors and the position of a vector relative to the coordinate axes.
4. What are the properties of dot product?
The different dot vector properties are here:
- Commutative Property: a . b = b. a
- Distributive Property: a. (b + c) = a . b + a. c
- Bilinear Property: a . (rb + c) = r.(a.b) + (a.c)
- Scalar Multiplication Property: (xa) . (yb) = xy(a.b)
- Orthogonal Property: Two vectors are orthogonal only when a.b = 0.