how to create the equation of a plane in 3D.?

Question

Ok, my task is to create the function of a plane that is perpendicular to the z axis and parallel to both x an y axes. It has to be perpendicular to one axes and parallel to the others, so the plane should be striaight, without angle of curvature. I don't know how to create the equation using either cartesian or parametric.

Please help me, can you show me how to do it manually? the reasoning I mean.

Answer 1

Consider a similar problem in 2 dimensions, but call the vertical axis "z" instead of "y". Like this:
z
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------------------------------------------------------------------- x
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Draw a line parallel to x and perpendicular to z (the solid line below):

z
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_________________ |_________________
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------------------------------------------------------------------- x
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z has a constant value, so anything like this would work:
z = 5, z=10, z=-2, etc.

Now imagine a y-axis coming straight out of the screen towards you. If you extend a plane through the line in the previous problem and keep it parallel to y (it is already parallel to x), you will notice that z does not change in this example, either. So the solution is the same!
z=5, z=10, z=-2, or z equals any constant value. The one exception to this might be z=0 because technically, the plane is not "parallel" to x or y because it is in the same plane as x and y.

Answer 2

in case you have 3 factors discover equation of planes And a Sphere Intersection of airplane with Sphere that's circle. discover equation of circle with the aid of replace z from airplane equation into Sphere equation put in sort (x-a)^2+(y-b)^2=r^2 (a,b) center r radius in case you have projection then from (x-a)^2+(y-b)^2=r^2 for 3 pairs of (px,py) projections acquire 3 equations with a,b,r to discover !!!

Answer 3

z=0

all the points in the x,y plane and hitting the z axis at 0, jsut liek the x,y plane does :P
hmmm its hard for me to explain how you do this, I suppose you jsut have to get 'used' to the 3d coordinate system, takes time.

Answer 4

The plane would be z= k, where k is the distance of the plane from the origin.