Plane parallel to the x axis.

Question

What does it mean for a plane to be parallel to the x axis (Or any other axis) ? And if the plane is parallel to the x axis for example wouldn't it also be in parallel to the y axis ? Could someone help me understand this ?

Answer 1

Let $\vec{n}(a,b,c)$ be a мусещк normal to the plane.

Thus, since $\vec{l}(1,0,0)$ is parallel to the $x$-axis we obtain: $$(1,0,0)(a,b,c)=0$$ or $a=0$.

Thus, we got an equation of our plane: $$by+cz+d=0,$$ where $b^2+c^2\neq0$.

If our plane is not parallel to $y$-axis then $b\neq0$.