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Vectores
Vectores
Vectores
Vectores
Vectores
Vectores
Vectores
Vectores
Vectores
Vectores
Vectores
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Vectores

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  • 1. VECTORES MODULO FÍSICA Sandra M. Pachón Peralta Lic. UPN 2014
  • 2. DEFINICIÓN Magnitud Dirección Sentido
  • 3. SISTEMA DE COORDENADAS LIBRES
  • 4. ALGEBRA DE VECTORES Adición libres A+B = b Sen α = ab / Sen θ = ab / Sen α = (Sen θ) / α θ a
  • 5. Adición coordenadas P x = P Cos α P y = P Cos θ P z = P Cos β Cos α = Ax+Bx /A+B Cos θ = Ay+By / A+B Cos β = Az+Bz / A+B A+B= i (Ax+Bx)+ j (Ay+By)+ k (Az+Bz) A+B =
  • 6. Diferencia libres A – B = A + (-B) A - B= β α θ Dirección Sen θ / A-B = Sen β /A = Sen α / -B
  • 7. Diferencia coordenadas A - B = i (Ax - Bx)+ j (Ay - By)+ k (Az - Bz) A-B =
  • 8. Producto punto o escalar, no se tiene coordenadas de referencia, ya que es la Combinación de 2 vectores para conseguir Un escalar asi: A. B = A B Cos θ θ Es conmutativo A.B = B.A A =0 ó B=0 A.B = 0 si θ = 90° ó θ = 270° A . A = A² , su ángulo es de 0
  • 9. Producto punto o escalar con coordenadas A . B = Ax.Bx + Ay.By + Az.Bz Es conmutativo A.B = B.A
  • 10. Producto vectorial o cruz Libres A X B = A x B Sen θ A X B = 0 si A = 0 ó B=0 θ = 0 es decir, A es paralelo a B Coordenadas i j k A x B = Ax Ay Az Bx By Bz
  • 11. Producto por un escalar libres b. B = C Si b > 0 tiene la misma dirección Si b< 0 tiene dirección contraria y sentido Producto por un escalar coordenadas bA = i(bAx) + j(bAy) + k(bAz) bA =

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