Three-Dimensional coordinate system

Question

Is the set $\left\{(x,y,z)|\ x\in \mathbb R,\ y=3,z=5\right\},$ a line or a plane?

When I draw them seperately they are surely planes. But when I combine them into one 3D graph does it become a line? If it does, Why doesn't it become a parallelipiped?

I'm reading the section on this matter and I wondered what if I combine them

Answer 1

Yes, if we are working on $\mathbb{R}^3$. Then $y=3$ is a plane and $z=5$ is another plane. And these planes are distinct and not parallel. Therefore, their intersection is a line.

Answer 2

This is a line. A parametric point of this set is $(x,3,5)$. Here $x$ is an independent parameter. So, as $x$ varies, becomes a line parallel to $x$-axis