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