Please give me one example of this.It also lies on an infinite number of lines
Please give me one example of this.And it lies in an infinite number of planes that contain any given one of the infinite number lines it lies on.
The line defined by the parametric equations {x=15t, y=15t, z=20t}Please give me one example of this.
I'll give you three: the x=10 plane, the y=15 plane, and the z=20 plane.Please give me one example of this.
I cant understand how can it be 3. If you say that x=10 is one representation then it means that you are considering y=z=0 which is not correct according to my above answers.I'll give you three: the x=10 plane, the y=15 plane, and the z=20 plane.
Although, I would admit that book example was way above my head, I would show you a simple example of room corner:“Those three planes are mutually perpendicular and intersect at the point (10,15,20).”
Actually my problem was solved when i was able to draw that point with the help of a room (cube) example. However i am not yet able to understand how can we have infinite representation of point. This would be a complex thing. 3d is similar to real world things and when we do measurements we usually specify 3 components and that points to a specific point and does not have infinite representations. When we say that points are not unique then we cant do any construction work in a real world environment.I think what he is looking for is the intersection of three planes where the three planes are explicitly predefined.
Probably he was interested in the planes that are PARALLEL to the three basic planes where either x,y, or z is zero.
So one plane would be parallel to the xy plane, one parallel to the xz plane, and one parallel to the yz plane. Then one 3d point would define those three planes.
Thanks, i drew this cube (room) and i am able to understand that point F is the intersection point for the 3 planes.Can you see that there is a plane that contains the x-axis as well as the point in question? If so, can you see that the same applies to the y-axis and the z-axis? Therefore we have three plans that interest at the point in question?
Actually in real world we use 3 quantities to represent volume similar to the 3 components of the point we just discussed and we use the unit cft (cubic feet). So it creates a confusion but you are right the 3 components of a point intersect each other at the defined cartesian coordinates but since its not a closed surface or polygon so a point's dimensions are not similar to volume.Volume of what? You haven't defined an enclosed volume? You are ASSUMING that this point defines SIX planes.
The similar situation in 2D should suffice. Take a piece of paper and put a point on it with a pen. Now draw a horizontal line and a vertical line that each go through that point. You now have two lines that can be used as a means of specifying that point. But now erase those two lines and draw a line coming down and to the right that goes through that point and another that is going up and to the left through that point. You now have two different lines that can be used as a means of specifying that point. If you put the original lines back on you now have four lines, any pair of which can be used to specify that point, giving you a total of six possibilities. Add a fifth line and you have added four more possibilities for a total of ten.Actually my problem was solved when i was able to draw that point with the help of a room (cube) example. However i am not yet able to understand how can we have infinite representation of point. This would be a complex thing. 3d is similar to real world things and when we do measurements we usually specify 3 components and that points to a specific point and does not have infinite representations. When we say that points are not unique then we cant do any construction work in a real world environment.
Take a rectangular room and use the floor as one plane and then build a wall from the center of each wall to the center of the opposite wall and use those as the other two planes. The intersection of those three places is the point on the floor in the center of the original room.So now my problem is that how a point can have multiple representation in a 3d environment. Kindly explain me with room picture i provided above.
Hi,
Thanks for your replies. It really removed the confusion.
Actually my problem was solved when i was able to draw that point with the help of a room (cube) example. However i am not yet able to understand how can we have infinite representation of point. This would be a complex thing. 3d is similar to real world things and when we do measurements we usually specify 3 components and that points to a specific point and does not have infinite representations. When we say that points are not unique then we cant do any construction work in a real world environment.
Thanks, i drew this cube (room) and i am able to understand that point F is the intersection point for the 3 planes.
Actually in real world we use 3 quantities to represent volume similar to the 3 components of the point we just discussed and we use the unit cft (cubic feet). So it creates a confusion but you are right the 3 components of a point intersect each other at the defined cartesian coordinates but since its not a closed surface or polygon so a point's dimensions are not similar to volume.
So now my problem is that how a point can have multiple representation in a 3d environment. Kindly explain me with room picture i provided above.
Zulfi.
In both these examples, the location of the point has not changed. It lies on the same plane in the centre of room's floor. How is the possible that a point can lie on infinite planes at the same time?Take a rectangular room and use the floor as one plane and then build a wall from the center of each wall to the center of the opposite wall and use those as the other two planes. The intersection of those three places is the point on the floor in the center of the original room.
Now take the original room but this time build two walls going from a corner of the room to the opposite corner. Where do these three planes intersect? At the point on the floor in the center of the original room.
If its an imaginary thing, its acceptable.You have to realize that, in a manner of speaking, mathematics is larger than the universe. By this i mean that we can calculate many things that will never be possible in the real universe we happen to live in. This means we have to have an application so that we can narrow down the math needed to solve the problem.
How is it possible for the same point to lie on an infinite number of lines at the same time?In both these examples, the location of the point has not changed. It lies on the same plane in the centre of room's floor. How is the possible that a point can lie on infinite planes at the same time?
Hi,
Thanks for taking pains in explaining me this.
In both these examples, the location of the point has not changed. It lies on the same plane in the centre of room's floor. How is the possible that a point can lie on infinite planes at the same time?
If its an imaginary thing, its acceptable.
Zulfi.
One another question is that tilting of sheet will change the angle but how its going to change the plane. The equation of plane does not contain any angle term. It has constants but again these constants do not depend upon angle. Please guide me.If we tilt the upper plane at a different angle, we would have another entirely different plane yet it would share the same 3d point
Thanks for helping me. You have solved my problem. I highly appreciate your efforts. You have explained me that same point can exist in multiple planes and this idea can be extended to infinite planes but now i have confusion with x, y, & z values and impact of angle on the equation of plane.For the plane we have:
a*x+b*y+c*z+d=0
by Aaron Carman
by Aaron Carman
by Aaron Carman
by Duane Benson