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Sumario Ecuaciones de la recta y el producto
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GEOMETRÍA EN EL ESPACIOECUACIONES DE LA RECTA
7
Punto A(x0 , y0 , z0) Vector director v (v1 , v2 , v3)
v vector Si no tienes el vector, con dos puntos de la recta puedes hallarlo AB
ECUACION VECTORIAL (x, y, z)= (x0, y0, z0) +t· (v1 v2 ,v3) t∊ℝ
https://marielmatesblog.wordpress.com/
Igualdad de vectores
x= xo +t· v1 PARA OBTENER PUNTOS DE
LA RECTA, BASTA CON QUE
ECUACION PARAMETRICA " y= yo +t· v2 t∊ℝ
DES VALORES A LA t
z= zo +t· v3
Despejo t e igualo
ECUACION CONTINUA x−xo = y−yo = z−zo
v1 v2 v3
Igualo dos a dos para obtener las dos ecuaciones
A1 x + B1 y + C1 z = D1 RESUELVE EL SISTEMA, PARA HALLAR
ECUACION IMPLICITA # PUNTOS DE LA RECTA (RECUERDA QUE ES
A2 x + B2 y + C2 z = D2 S.C.I. – 1 PARAMETRO)
ECUACIONES DEL PLANO
Punto A (x0 , y0 , z0) Dos vectores u(u1 , u2 , u3) y v(v1 , v2 , v3)
ECUACION VECTORIAL (x, y, z)= (x0 , y0 , z0) + t · (u1 , u2 , u3) + s · (v1 , v2 , v3 )
x= xo + t· u1 + s · v1
ECUACION PARAMETRICA " y= y + t· u + s · v
o 2 2
z= zo + t· u3 + s · v3
ECUACION IMPLICITA x−xo y−yo z−zo
Ax+By+Cz=D u1 u2 u3 =0
Vector ⃗n
Vector ⃗n = ⃗u x ⃗v
Vector ⃗n = (A , B , C) v1 v2 v3
normal ⃗v
Punto A
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