Question 1

What is a Vector Dot Product?

Accepted Answer

The dot product (scalar product) of two vectors produces a scalar — a single number — by summing the products of corresponding components. It encodes both the magnitudes of the vectors and the cosine of the angle between them, making it essential for computing projections, work done by a force, lighting in computer graphics, and similarity in machine learning.

References

Question 2

How does the Vector Dot Product work?

Accepted Answer

u · v = u₁v₁ + u₂v₂ + u₃v₃ + ... (sum of component products) Then: u · v = |u| × |v| × cos(θ) Then: θ = arccos(u·v / (|u|×|v|)) — angle between vectors Then: u · v = 0 ⟺ vectors are perpendicular (orthogonal).

Question 3

Can you give an example of how to use the Vector Dot Product?

Accepted Answer

Example: Input u=(3,4,0), v=(4,3,0) gives a result of u·v = 12+12+0 = 24, |u|=5, |v|=5, θ=16.3°.

Question 4

Is the Vector Dot Product free to use?

Accepted Answer

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

Question 5

How accurate is the Vector Dot Product?

Accepted Answer

Our Vector Dot Product uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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