Math & Algebra Tool
Dot Product Calculator
Calculate the scalar product of two vectors in 2D or 3D space.
x
y
z
x
y
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Scalar Result (A · B)
0
Σ The Formula
A · B = ∑ (A_i × B_i)
Real World Examples
2D Vectors
[2, 3] · [4, -1] = (2×4) + (3×-1) = 5.
Orthogonal Vectors
[1, 0] · [0, 1] = 0 (means they are perpendicular).
# About This Calculator
The Dot Product (or scalar product) is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.
It is fundamental to physics and engineering for:
- Calculating work (Force · Displacement).
- Determining the angle between two vectors.
- Projecting one vector onto another.
How To Use
- Choose the **Dimension** of your vectors (2 or 3).
- Enter the components for **Vector A**.
- Enter the components for **Vector B**.
- The **Dot Product** scalar value is calculated instantly.
Frequently Asked Questions
What does it mean if the dot product is zero?+
If the dot product of two non-zero vectors is zero, it means the vectors are orthogonal (perpendicular) to each other.
Is dot product the same as cross product?+
No. Dot product results in a scalar (a single number), while cross product results in a vector (a direction in 3D space).
Is Dot Product Calculator free to use?+
Yes, Dot Product Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.
How accurate is Dot Product Calculator?+
We use standard mathematical formulas and high-precision computing algorithms to ensure results for Dot Product Calculator are accurate for academic and professional use.
Can I use Dot Product Calculator on my phone?+
Yes! Dot Product Calculator is fully responsive and optimized for all devices, including smartphones, tablets, and desktops.
Do you save my data?+
No. We prioritize your privacy. All calculations are performed in your browser or temporarily processed, and we do not store your personal input data.
About
The Dot Product (or scalar product) is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.
It is fundamental to physics and engineering for:
- Calculating work (Force · Displacement).
- Determining the angle between two vectors.
- Projecting one vector onto another.