As the title suggests, is Vector arithmetic (including Cross and Dot Products and Length Calculations) compatible between 2D and 3D Vectors where a "2D Vector" is a 3D Vector with a third parameter that is always one (1)?
That is, is $\vec{A}$(x, y, 1) compatible with $\vec{B}$(x, y, z) where $\vec{A} + \vec{B} = \vec{C}$ and $\vec{C} = (Ax + Bx, Ay + By, 1)$; (etc for all basic arithmetic); $\vec{A} \cdot \vec{B} = \vec{C}$ and $\vec{C} = Ay \times 1 - 1 \times By, 1 \times Bx - Ax \times 1$; and $\vec{A} \times \vec{B} = x$ where $x = Ax * Bx + Ay * By + 1 * 1$ as well as $\lVert A \rVert = \sqrt{(Ax^2) + (Ay^2) + (1^2)}$ and $\lVert B \rVert = \sqrt{(Bx^2) + (By^2) + (1^2)}$
Will this produce inaccurate results?