The planes \(ax+by+cz+d=0\) and \(a^{\prime}x+b^{\prime}y+c^{\prime}z+d^{\prime}=0\) are parallel to each other, if

\(\frac{a}{a^{\prime}}=\frac{b}{b^{\prime}}=\frac{c}{c^{\prime}}\) \(\frac{a}{a^{\prime}}=\frac{b}{b^{\prime}}=\frac{d}{d^{\prime}}\) \(aa^{\prime}+bb^{\prime}+cc^{\prime}=0\) \(aa^{\prime}+bb^{\prime}+cc^{\prime}+dd^{\prime}=0\)

\(\frac{a}{a^{\prime}}=\frac{b}{b^{\prime}}=\frac{c}{c^{\prime}}\)

Recall the condition of two planes being parallel