The "intersection" you are talking about is imaginary, and in my explanation it is called the instant center. It is the axis arond which the body rolls on turns. It can be, and usually is different at the front axle, than it is at the rear.
The plane of the ball joint centerline, or the king pin axis, will normally be outside the plane of the outer tie rod end on a rear steer, this is correct according to the Ackerman principal. Below is a drawing showing how Ackerman is figured.
Ackerman is rarely totally correct, nor does it have to be. Without Ackerman one of the front tires will scrub, or slide sideways on a turn, more or lees depending on the radius of the turn. Also tires have a slip angle, an angle somewhere between the degree of turn, and straight ahead, which the tire will slide in a turn, and this angle depends on the traction, and the tire construction. Radials as a group, have a different slip angle than bias tires. This can be taken into account when figuring Ackerman. Also the same spindle may be used on several vehicles with a different wheelbase. The basic spindle used on a GM pickup mat be used on trucks with a wheelbase of from 105" to 167". Obviously the Ackerman won't be the same for all, and in use may not be exactly correct for any of them. So usually 75% Ackerman is generally acceptable.
I hope this answered your question