Answer:
The equation x=z in the space, will be the Identity straight line on the plane xz, inside the R³ space for all y values. This represents an infinite plane.
Step-by-step explanation:
First we must know that R³ mathematically means that we have three straight lines of real numbers, disposed as a cartesian system, this means that it represents a space of 3 dimensions.
Then, as the equation is x=z, this means that <em>all points where x=z will form a straight line</em>, and this straight line will "live" in the xz plane, for all values of y, as it is not restricted in the problem.
Finally, <u>the equation x=z represents an Identity straight line on the plane xz</u>, to imagine this, put numbers into the equation, then you will have for example that x=1=z=1 (which is the point (1, 1) in the plane xz, and (1, 0, 1) in the space R³). If you replace the infinite points, you will get the Identity straight line in the plane xz, and represented inside the space R³ for all values of y, which finally represents an infinite plane.
