Vector Dot Product Calculator

Calculate the dot product of two vectors. Free online vector dot product calculator.

The Vector Dot Product Calculator computes the scalar (dot) product of two vectors. The dot product a·b = |a||b|cos(θ) measures how much vectors point in the same direction. Enter vector components to find the dot product and the angle between vectors. Essential for physics, graphics, and machine learning.

Common use cases

  • Work calculation in physics (F·d)
  • Testing vector orthogonality
  • Projection calculations
  • Computer graphics lighting
  • Machine learning similarity

How to use

  1. Enter components of Vector A
  2. Enter components of Vector B
  3. Click calculate for dot product
  4. View the component-wise multiplication
  5. See the angle between vectors

FAQ

What is the dot product?

a·b = a₁b₁ + a₂b₂ + ... (sum of component products). Alternatively, |a||b|cos(θ).

What does dot product = 0 mean?

The vectors are perpendicular (orthogonal). This is the test for perpendicularity.

What's the geometric meaning?

Dot product measures 'how parallel' vectors are. It's |a| times the projection of b onto a's direction.

Is dot product commutative?

Yes, a·b = b·a.