Projection image/Point/Preimage/Exercise

Let a linear mapping ${}\varphi \colon \mathbb {R} ^{3}\rightarrow \mathbb {R} ^{2}$ as in example be given, in order to represent three-dimensional shapes in the plane. Imagine the preimage for a point ${}P\in \mathbb {R} ^{2}$! How do the corresponding line equations look like? What points ${}Q\in \mathbb {R} ^{3}$ have the same image point as the corner ${}(1,1,1)$ of the unit cube?

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