Good Day: The question I have is for figuring the distance from one planetary object to another. I suppose it could be middle or secondary for status, as I don't know what level of math is taught when. I also guess I would classify as an 'other'. The question is: how do I figure out the distance of one object in 3D space to another object in 3D space? I have an object at say x = 5.872, y = 2.876, and z = 7.290; and the other object is at x = 1.129, y = 8.213, and z = 11.127. I have been suggested to use the pythagorean theory on this, but since there are three variables, I don't understand how. David Hi David,
Suppose that you have two points A and B in 3space as in the diagram below.
Construct a rectangular box with edges parallel to the axes and with the line AB a diagonal of the box as in the diagram below.
Since the triangle ADB is a right triangle, the theorem of Pythagoras gives If A = (x_{1}, y_{1}, z_{1}) and B = (x_{2}, y_{2}, z_{2}) then C = (x_{1}, y_{2}, z_{1}) and D = (x_{1}, y_{2}, z_{2}) and Penny
