\text{Nutná podmienka rovnobežnosti }a,α: (a\cap α=\empty)⇒(∃a'=a;a∥a') . 

$ \pmb π $

$α$

$\pmb α$

$\math{\pmb α=\small (K,L,M)} \text{ - rovina }$

$\pmb A$

$a$

$\math {P_\pmb a}$

$\math{\pmb a: a \parallel α }\text{ a zároveň }a \cap α=\empty $

$\math {\pmb P}$

\text{zvoľme bod }P∈α

\text{ a rovinu}

$a'$

$\math{\pmb β:( β=(a,P),P \in α);a'= β \cap α}$

\text{Dôkaz }a' \cap a=\empty \text{ nepriamo }

\text{∙ existuje bod: }R=a'\cap a⇒R∈α\cap a

\text{∙ priamka }a \text{ nie je rovnobežná s } α

K = (3, -4, 0)
O = Intersect(yAxis, zAxis)
L = (3, 7, 0)
N = (-2.8190296749019392, -1.317815288138405, 0)
p = Plane(N, K, L)
M = (-0.4182521221790143, -2.736853408926894, 4.380977056829263)
α = Plane(K, L, M)
E = PointIn(α)
f = Line(K, L)
b = false
g = OrthogonalLine(M, f, space)
A = (2.355939360354391, 0.46431904186762907, 3.253388060104223)
h = Line(A, g)
P_a = Intersect(h, p)
a = false
P = PointIn(α)
q = Plane(P, h)
i = Line(P, h)
c = false