Geometria v rovine

Určte \(m\in \mathbb{R}\) tak, aby priamka \(p\colon x - 2y + 7 = 0\) bola rovnobežná s priamkou \(q\colon mx + 3y - 11 = 0\).

Určte \(m\in \mathbb{R}\) tak, aby priamka \(p\) \[ p\colon x = 1 + t,\ y = -3t,\ t\in \mathbb{R} \] bola rovnobežná s priamkou \(q\) \[ q\colon x = 3 - 2u,\ y = 1 + mu,\ u\in \mathbb{R}. \]

Určte \(m\in \mathbb{R}\) tak, aby priamka \(p\colon 3x - y + 17 = 0\) bola rovnobežná s priamkou \(AB\), kde \(A = [2;1]\), \(B = [m;0]\).

Určte \(m\in \mathbb{R}\) tak, aby priamka \(p\colon x = 1 + mt,\ y = 2 - 3t,\ t\in \mathbb{R}\) bola rovnobežná s priamkou \(q\colon x + 4y - 3 = 0\).