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Rovina


SV�T GEOMETRIE


Norm�lov� vektor, obecn� tvar rovnice


Norm�lov� vektor n = (A, B, C)

Nerovnob�n� vektory le��c� v rovin� s1 = (a1,b1,g1) a s2 = (a2,b2,g2

Obecn� tvar rovnice: Ax + By + Cz + D = 0


1. Po a vektor n :

A (x - x0) + B (y - y0) + C (z - z0) = 0


2. Po a s1 a s2

a)� n = s1 x s2� a (1)

b) Parametrick� tvar :


3. T�emi body (nele��c�mi na p��mce) Po, P1, P2. Ur�it n = Po P1 x Po P2 a (1)


4. Pr�se��ky s osami sou�adnic (�sekov� tvar):


P��klad:

Po = [2, 4, -1], p1 = (2, 3, -1), p2 = (1, -1, 2)

Po = [2, 4, -1], s1 = (1, -2, 4), s2 = (-3, 3, -1)

Po = [2, 4, -1], w1 = (-3, -5, -2), w2 = (2, 2, -1)

pr�se�nice ve stejn�m bod� Po

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