Distance between a point and a plane along a line

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MattC

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I have two points on a line that are D units apart from each other. The line has a plunge and trend of LP to LT. Assume that the first point is at the origin (0, 0, 0)

Thus, the x, y, z of the second point are:

X = sin(LT+180) * sin(LP) * D
Y = cos(LT+180) * sin(LP) * D
Z = cos(LP) * D

I want the upwards direction so I am adding 180 to the trend.

At the second point, there is a plane with the plunge and trend of JP to JT.

I want to find the minimum distance between the first point and the plane.

If I used the following formula:

Minimum distance = ABS( sin(JP)*sin(JT)*X + Sin(JP)*cos(JT)*Y + cos(JP)*Z)

Is that going to give me the correct answer?
 
It seems to me there is something missing. Plunge and Trend are suffient to determine a line, but how are they sufficient to determine a plane? To measure the MINIMUM distance to a plane, you must have a Unit Normal Vector, not just any vector. Therein lies the problem. Is the vector <X,Y,Z> Normal to the plane at (X,Y,Z)? If not, then your answer is no. Again, with only plunge and trend at (X,Y,Z), how is that a unique plane? Maybe I'm just missing something.
 
Forget the first post, I’ll try it from another direction.

I have:
-Plunge and trend of a line
-Distance along the line to the next point

I’ll assume that the first point, P1 is at the origin, thus I can get the coordinates of the second point.

So, I know:
-Coordinates of two points, P1, P2
-Normal vector of a plane, n, which travels through P2


I want to find the minimum distance from P1 to the plane at P2.

Is this possible? Thanks in advance.
 
I'm glad you grought this one back up. I had forgotten tha tI wanted so say something else about it.

My last question, "Is ti Normal" is a little silly. If it is, the distance obviously would be D.

As for your revised question, why isn't the distance just the distance between the two points?
 
It's not the distance between the two points (which, is actually known) but I'll describe a visual way as maybe it will help.

Using a ruler (or something long), set it on the table at any trend and plunge. Assume that the plane is the table. I want to find a way to figure out the minimum distance between the top of that ruler (P1, the origin) and the table (P2 represents the bottom of the ruler and it also is a point in the known plane).

The table is a simplified case, the actual plane can be in any direction.

Did I explain that well enough....does this make more sense?

Thanks again
 
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