π₁ : x − y + 2z = 1 π₂ : x + 2y + 3z = 2

Wektor normalny 1 prostej: a = [1, −1, 2]

Wektor normalny 2 prostej: b = [1, 2, 3]

$\cos \propto = \frac{ab}{\left| a \right||b|}$ ab = [1,−1,2][1, 2, 3]=5

$$\left| a \right|\left| b \right| = \sqrt{1 + 1 + 4}\sqrt{1 + 4 + 9} = 2\sqrt{}21$$

$$\cos \propto = \frac{5}{2\sqrt{}21}$$

$$\propto = arccos\frac{5}{2\sqrt{}21}$$