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Prove that the four points 1 3 1 and 1 1 -1 and -1 1 1 and 1 2 1 are lying on the same plane?
False. Over constrained, and not defining a single flat plane of the form:
Ax+By+Cz+D=0
Wolfram-Alpha inputs for the first 3 and last 3 sets of coordinates:
plane through (1,3,1) and (1,1,-1) and (-1,1,1)
plane through (1,1,-1) and (-1,1,1) and (1,2,1)
define different equations => different planes => therefore all 4 points do NOT lie on a common plane.
What else can I help you with?
What are the names of four coplaner points?
coplaner points- are points lying on his the same plane,.. solution: plane R contains XY XY contains X and Y...
Can there be four points in one plane?
There can be any number of points on a plane, or even on a line - and any number of lines on a plane.
How many planes can be formed with four non collinear points?
Four non-collinear points can form exactly one plane. This is because a plane is defined by three non-collinear points, and adding a fourth point that is not in the same line as the other three does not create a new plane; rather, it remains within the same plane defined by the initial three points. Therefore, all four points lie in the same unique plane.
What Four points are always coplanar if they?
If they lie in the same plane.
Are four collinear points also coplanar?
Yes, four collinear points are also coplanar. Collinear points lie on the same straight line, and any set of points that includes at least three points can be contained within a plane. Therefore, since collinear points can be defined within a single plane, four collinear points must be coplanar.
What are the names of four coplaner points?
coplaner points- are points lying on his the same plane,.. solution: plane R contains XY XY contains X and Y...
Is it true that the four coplanar points determine three unique plane?
No. If the four points are coplanar, they determine only one plane!
Can there be four points in one plane?
There can be any number of points on a plane, or even on a line - and any number of lines on a plane.
When are four points in a plane?
Any 4 points can lie in a plane, 3 points determine a plane and just take the 4th to be say the origin.
Four regions of a coordinate plane?
points
Can four points be in the same plane?
yes
How many planes can be formed with four non collinear points?
Four non-collinear points can form exactly one plane. This is because a plane is defined by three non-collinear points, and adding a fourth point that is not in the same line as the other three does not create a new plane; rather, it remains within the same plane defined by the initial three points. Therefore, all four points lie in the same unique plane.
Four points are always coplanar if?
all of them are collinear they lie in the same plane
What Four points are always coplanar if they?
If they lie in the same plane.
Are four collinear points also coplanar?
Yes, four collinear points are also coplanar. Collinear points lie on the same straight line, and any set of points that includes at least three points can be contained within a plane. Therefore, since collinear points can be defined within a single plane, four collinear points must be coplanar.
Four points are always coplanar if they?
lie on the same plane and are collinear
Four points are alwats coplanar if they?
-lie in the same plane -are collinear
