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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}]

I got a line and not a plane

and:

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

Again the same issue, and this time is worse than before

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!

Thank you in advance!

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A plane is a two dimensional object (embedded in 3D), so it needs two parameters, u,v to form a linear combination of two non-parallel vectors.

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

ParametricPlot3D[ u vx + v vy, {u, -1, 1}, {v, -1, 1}]
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    $\begingroup$ Which was doubtless the point of the teacher asking to do a parametric plot! $\endgroup$
    – murray
    Nov 23, 2018 at 18:12

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