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Este artículo presenta una deducción para la expresión del módulo resultante de dos vectores (véase vector (física) y módulo (vector)) de un espacio vectorial (sobre los números reales).
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Demostración de ley del coseno en vectores
33. Cálculo vectorial: Ángulo entre vectores, demostración de fórmula.
Teorema de De Moivre. Demostración
Transcription
Deducción
Sean dos vectores y que forman un ángulo entre
sí:
La fórmula para calcular se deduce observando los triángulos rectángulos que se forman, OCB y ACB, y aplicando el Teorema de Pitágoras. En el triángulo OCB:
Resultando:
En el triángulo ACB :
Sustituyendo esto en la igualdad de antes resulta: