Vectors - Unit Vectors

A plane \(\Pi \) has an equation of \(\mathbf{r}\cdot \mathbf{n}=k\).

1. If the origin is on the plane explain how the value of \(k\) could be determined and state its value.
2. State the unit vectors of the normal of \(x-y\), \(y-z\) and \(x-z\) planes. Thus, find the equations of each plane.
3. Show that the shortest distance of plane \(\Pi \) to the origin is \(\frac{\left| k \right|}{\left| \mathbf{n} \right|}\).