# How to draw a plane with ParametricPlot3D when f(x,y)==0?

I have the same issue (actually I have exactly the same prompt) as the creator of this topic: Draw two planes of Cartesian equation: y=3-x and z=2+x with Plot3D

The answer I found there was really useful, but it is not valid for me because my teacher asked me to plot the plane by using "ParametricPlot3D".

The parametric equation of my function is:

x= k+1, y= 2-k, z= 3+k


and its cartesian equation is:

y= 3-x,z= 2+x


The main difficulty with this exercise is that "z" (better known as "f[x,y]") is equal to 0, so I can´t inject f[x,y] into ParametricPlot3D.

I already spent hours and hours trying to do this, but I couldn´t get it. Here are my best tries so far:

ParametricPlot3D[{k + 1, 2 - k, k + 3}, {k, -10, 10}, AxesLabel -> {x, y}]


and:

ParametricPlot3D[{k + 1, 2 - k, 0}, {k, -10, 10}, PlotStyle -> Blue,
AxesLabel -> {x, y, z}]


However, I'm only able to get lines and not planes. I've reviewed many times Wolfram's Mathematica documentation, but I just can´t get the software to plot a plane with ParametricPlot3D!

vx = Normalize[{1, 2, 3}]; vy = Normalize[{3, 2, 0}];