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Sometimes.
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Can 3 points be non-coplanar is outside the plane?
If you are given a plane, you can always find and number of points that are not in that plane but, given anythree points there is always at least one plane that goes through all three.
A line and a point not on the line are never coplanar?
No, they always are From Wikipedia.org, "The World's Encyclopedia" when I searched coplanar In geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. For example, three distinct points are always coplanar; but four points in space are usually not coplanar. Since 3 points are always coplanar. A point and line are always coplanar
Can one plane sometimes pass through three noncollinear points?
no
A line passing through two distinct points in one plane lies completely in that plane?
Always
What is the set of all points on a plane so that the sum of the distances from two fixed points is always constant?
an ellipse.
Does a plane containing two points of a line always never or sometimes contain the entire line?
It contains the whole line.
Does A line passing through two distinct points in one plane always sometimes or never lie completely in that plane?
Always; although that line can lie in infinitely many planes.
Does a line passing through two distinct points in one plane sometimes lies in that plane?
it always lies in that plane
Are a line and a plane that do not intersect always sometimes or never skew?
A line and a plane that do not intersect are always skew. Skew refers to two or more lines or planes that are not parallel and do not intersect. Since a line and a plane are different-dimensional objects, they will never intersect and will always be skew.
What is coplanar points?
Definition of Coplanar points: Coplanar means that the points are on the equal plane. Plane is a two-dimensional object, with as such is a bit more complicated.Collinear,line,plane and point are the related terms of coplanar.Points that are on the same plane. 2 points are alwayscoplanar...3 points are always coplanar...4 points are sometimes coplanar.
If two lines intersect then they lie in one plane. Is this true always sometimes or never?
always. if two lines intersect, then exactly one plane contains the lines.
Can 3 points be non-coplanar is outside the plane?
If you are given a plane, you can always find and number of points that are not in that plane but, given anythree points there is always at least one plane that goes through all three.
Is an imaginary number always sometimes or never a complex number?
Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.
Do three distinct points always lie on the same plane?
Yes. That's why a 3-legged stool never wobbles.
Do 3 distinct points always lie on the same plane?
Yes. That's why a 3-legged stool never wobbles.
Four points are always coplanar?
No. For any three points it is always possible to find a plane on which they all lie. A fourth point is most unlikely to be coplanar with the first three unless it is deliberately placed to be so.
Are a plane and a point not on the plane always coplanar?
No. In order to be coplanar, points have to be in the line.
