I got this from an elementry formula, I will not derive it here. I'll just write it down:
For the distance D between a point and a plane
, where, in our case, are the coefficients of the terms of the plane
The distance between and melbourne was calculated by the formula I wrote above. The distance between and Earth is the same as the distance between and melbourne since can be expressed as a normal vector
To find the melbourne point we can draw from the origin of our coordinate system, a vector with the terminal end meeting the plain at the melbourne point . and therefore, also meeting the tail of . We can draw another vector from the origin to the point . From we draw a vector . to . Since is on the surface of the plane, it is perpendicular to . We may write:
Now all we have to do is solve the vector equation for . I will leave that to you.