Hi,
Thanks for your reply. Its very useful. What i understood is that: x, y & z values in 3d plane equation tell us about the width, length and the depth of plane where as coefficients A, B, C, & D deal with its orientation from the ___?_________. Each plane has its own access (am i right?). I think this is a different concept and I want to start another thread to discuss the details of it. I want to thank both of you for your time & effort.

Zulfi.

 

Hi,
Thanks for your reply. Its very useful. What i understood is that: x, y & z values in 3d plane equation tell us about the width, length and the depth of plane where as coefficients A, B, C, & D deal with its orientation from the ___?_________. Each plane has its own access (am i right?). I think this is a different concept and I want to start another thread to discuss the details of it. I want to thank both of you for your time & effort.

Zulfi.

A plane is a mathematical construct. It has now width or length (it is infinite in extent) and it has no depth (its thickness is zero).

Again, start from the easier to visualize two-dimensional situation.

A line is a set of points that satisfy the following equation:

y = mx + b

This can be generalized to

ax + by + c = 0

Do you see how? Hint: Work it from this equation back to y=mx+b.

It is meaningless to talk about the thickness of a line, or of its length. It has zero thickness and it is infinitely long.

Any point that satisfies the defining equation given above is, by definition, part of the line (or "lies" on the line). If a particular point does not satisfy that equation, then it doesn't.

When you add another dimension, your line becomes a plane and the defining relation gets another dimension, so it becomes

ax + by + cx + d = 0

Any point that satisfies this equation is on the plane and any point that doesn't is not.

It really is that simple.

From here we can start asking a lot of useful questions such as whether a particular line is in the plane and, if not, whether it intersects the plane at all. We can also ask whether two planes intersect each other and, if they do, what is the line that they share? Lots of other questions can be asked and answered, but first you have to understand the basic definition of a plane.

 

Hi,
Thanks for your reply. Its very useful. What i understood is that: x, y & z values in

3d plane equation tell us about the width, length and the depth of plane where as

coefficients A, B, C, & D deal with its orientation from the ___?_________. Each plane

has its own access (am i right?). I think this is a different concept and I want to

start another thread to discuss the details of it. I want to thank both of you for

your time & effort.
Zulfi.

Hi,
The constants a,b,c,d define the plane, the variables x,y,z just tell you where the
point in the plane is.
So if a,b,c,d are equal respectively to 1,2,3,4, then that is one plane, but if they
are equal to 1,2,3,5, that is an entirely different plane, without even looking at
x,y,z yet.
If you wanted to generate a lot of points in a plane you could just generate numbers
for x, y, and z, after selected a plane with a,b,c,d.
For example, solving for z again we have:
z=-(a*x+b*y+d)/c
and selecting a plane with a,b,c,d equal to 1,1,1,1, we have:
z=-(x+y+1)
and to see some points one this plane we would do the following:
for y=-10 to +10 do
for x=-10 to +10 do
z=-(x+y+1)
plot(x,y,z)
end for
end for
So for every y we are stepping through values for x from -10 to +10, so that is -10,-
9, -8, etc., to +10,
and then we step y again and repeat all the x again. this gives us 400 points on the
plane spaced 1 unit apart.
If we stepped by 0.1 then we would get more points all spaced 0.1 units apart.
If we change any of the a,b,c,d though and repeat the above steps, we see a different

set of points that belong to a different plane.
So we define the plane with a,b,c,d, and we find points by using x,y, and solving for
z for example.

 

Hi,
Thanks. I am reading that but i cant verify this right now. So i would discuss this in another thread. Thanks for your cooperation and time.

God bless you.

Zulfi.