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Can you show that 2 Points Determine a Plane?

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We have all heard that "3 Points Determine a Plane" Meaning 3 Distinct Non-Collinear Points in 3-Space Using the same ideas - Can you show that: 2 distinct Points Determine a ...show more
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no, because they don't.
2 points determine a line.
and there are an infinite number of planes that contain that line.
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  • Geezah answered 7 years ago
    No, because you need at least three points to define a plane.

    Look at a corner in the room you're in, where two different walls meet. Take a pencil and mark two points on the corner. If you think of the walls as two planes, then you have two different planes that contain the two points you marked. Therefore, you can't have 2 points define a plane.

    Similarly, look up at the ceiling where two walls and the ceiling meet in the upper corner. That's a point common to THREE different planes. So 1 point doesn't determine a specific plane.
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  • Burhop answered 7 months ago
    Yes. One point is on the plane, the second point is above it defining a vector (line) perpendicular to the plane.

    Many people falsely assume the points must be on the plane (like a camera tripod) so it must take three. The two point analogy is more like a nail thought a board with the two points at each end of the nail.
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  • Pointy answered 7 years ago
    Two points can never determine a plane ... they can only form a straight line as in "two points determine a straight line."

    And, of course, a point is just a point. It cannot be a line nor can it be a plane. However, a point can be on a line and on a plane.
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  • rhsaunders answered 7 years ago
    They don't. Two points detremine a line, and there are an infinite number of planes which include the line.
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  • Hell C answered 7 years ago
    I can show it but with a assumption that they don't lie on a line passing through origin :P. This is bit of cheating but its interesting. consider two different points with co-ordinates (x1, y1, z1) and (x2, y2, z2). and they are linearly independent. then they can span a plane
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  • Can you show that 2 Points Determine a Plane?
    We have all heard that "3 Points Determine a Plane"
    Meaning 3 Distinct Non-Collinear Points in 3-Space

    Using the same ideas - Can you show that:

    2 distinct Points Determine a Plane

    or better

    1 Point Determines a Plane





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