Introduction to non-coplanar points:
The points which do not lie in the same plane or geometrical plane are called as non-coplanar points. Any 3 points can be enclosed by one plane or geometrical plane but four or more points cannot be enclosed by one. The points belong to the same plane are called as coplanar points. In this article we shall be discussing the non-coplanar points. Now we know what non-coplanar point is and we shall see some examples of the non-coplanar points and solve it for the same.
Example for Non Co-planar Points
1) From the below shown figure the points are non coplanar points as they do not lie on the same plane it lies in different planes.
2) We can see four planes with the help of four non co-planar points.
3) Plane is the two dimensional geometrical object.
Non co-planar points
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Solved Examples for Non Co-planar Points:
Ex 1: Check whether the following lines are co-planar or not.
3x+6y+9 = 0 and 4x+4y+11 = 0
Sol : The given equations are 3x+6y+9 = 0 and 4x+4y+11 = 0
The slope intercept form can be given as y = mx+b
Where m indicates slope.
Comparing the above equation with the given equation, we get:
6y = -2x-9
Dividing by 6 on both sides we get:
We get,
--- (1)
The slope intercept form can be given as y = nx+b
Where n indicates slope.
Comparing the above equation with the given equation, we get:
4y = -4x-11
Dividing by 4 on both sides we get:
y = -1
We get n = -1--------- (2)
Equation (1) (2), that is m n
That is the slopes of the two equations are not equal and therefore the points lie on the two lines are non co-planar points.
Ex 2: Check whether the following lines are co-planar or not.
x+5y+9 = 0 and 2x+10y+11 = 0
Sol : The given equations are x+5y+9 = 0 and 2x+10y+11 = 0
The slope intercept form can be given as y = mx+b
Where m indicates slope.
Comparing the above equation with the given equation, we get:
5y = -x-9
Dividing by 5 on both sides we get:
We get,
------- (1)
The slope intercept form can be given as y = nx+b
Where n indicates slope.
Comparing the above equation with the given equation, we get:
10y = -2x-11
Dividing by 10 on both sides we get:
We get
--------- (2)
Equation (1) =(2), that is m = n
That is the slopes of the two equations are equal and therefore the points lie on the two lines are co-planar points.
The points which do not lie in the same plane or geometrical plane are called as non-coplanar points. Any 3 points can be enclosed by one plane or geometrical plane but four or more points cannot be enclosed by one. The points belong to the same plane are called as coplanar points. In this article we shall be discussing the non-coplanar points. Now we know what non-coplanar point is and we shall see some examples of the non-coplanar points and solve it for the same.
Example for Non Co-planar Points
1) From the below shown figure the points are non coplanar points as they do not lie on the same plane it lies in different planes.
2) We can see four planes with the help of four non co-planar points.
3) Plane is the two dimensional geometrical object.
 |
| Non co-planar points |
Non co-planar points
Stuck on any of these topics super hard math problems, any math problem solver try out some best math website like mathsisfun, mathcaptain.com and math dot com.
Solved Examples for Non Co-planar Points:
Ex 1: Check whether the following lines are co-planar or not.
3x+6y+9 = 0 and 4x+4y+11 = 0
Sol : The given equations are 3x+6y+9 = 0 and 4x+4y+11 = 0
The slope intercept form can be given as y = mx+b
Where m indicates slope.
Comparing the above equation with the given equation, we get:
6y = -2x-9
Dividing by 6 on both sides we get:
We get,
--- (1)
The slope intercept form can be given as y = nx+b
Where n indicates slope.
Comparing the above equation with the given equation, we get:
4y = -4x-11
Dividing by 4 on both sides we get:
y = -1
We get n = -1--------- (2)
Equation (1) (2), that is m n
That is the slopes of the two equations are not equal and therefore the points lie on the two lines are non co-planar points.
Ex 2: Check whether the following lines are co-planar or not.
x+5y+9 = 0 and 2x+10y+11 = 0
Sol : The given equations are x+5y+9 = 0 and 2x+10y+11 = 0
The slope intercept form can be given as y = mx+b
Where m indicates slope.
Comparing the above equation with the given equation, we get:
5y = -x-9
Dividing by 5 on both sides we get:
We get,
------- (1)
The slope intercept form can be given as y = nx+b
Where n indicates slope.
Comparing the above equation with the given equation, we get:
10y = -2x-11
Dividing by 10 on both sides we get:
We get
--------- (2)
Equation (1) =(2), that is m = n
That is the slopes of the two equations are equal and therefore the points lie on the two lines are co-planar points.
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