Can 3D co-ordinates be transferred into 2D co-ordinates? Is it possible to transform co-ordinates $(a,b,c)$  into $(x,y) $ such that $(x,y)$  is unique for each $(a,b,c)$ ? $a, b,  c,  x,  y$ are in $\Bbb{R}$ .

It's is possible to have a bijection between $\mathbb{R}^3$ and $\mathbb{R}^2$, since it can be shown that $\mathbb{R}$ and $\mathbb{R}^2$, and hence every $\mathbb{R}^n$ has the same cardinality.  But a linear or affine isomorphism is not possible if the dimensions are different.
