Calculadora de Producto Escalar (Producto Punto)
Calcula el producto punto de dos vectores en 2D o 3D. Ingresa las componentes y obtén el resultado escalar al instante de forma gratuita.
Dot
32.0000
Mag A3.7417
Mag B8.7750
Angle12.9332 deg
Fórmula
Dot Product
Formula
A · B = a₁b₁ + a₂b₂ + a₃b₃
Geometric Interpretation
A · B = So: theta = arccos(A · B / (A × B × cos(theta) A × B
Properties
Ejemplo Resuelto
Dot product of (1,2,3) and (4,5,6).
- 01A · B = 1×4 + 2×5 + 3×6 = 4 + 10 + 18 = 32
- 02|A| = √(1+4+9) = √14 ≈ 3.742
- 03|B| = √(16+25+36) = √77 ≈ 8.775
- 04cos(theta) = 32/(3.742 × 8.775) ≈ 0.9746
- 05theta ≈ 12.93°
Preguntas Frecuentes
What is the dot product?
The dot product is a way to multiply two vectors to get a scalar (single number). It measures how much two vectors point in the same direction.
When is the dot product zero?
The dot product is zero when the vectors are perpendicular (orthogonal). This is a common test for perpendicularity.
What is the difference between dot product and cross product?
The dot product gives a scalar and measures alignment. The cross product gives a vector perpendicular to both inputs and measures the area of the parallelogram they span.
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