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Good question!! Well, one way to visualize three planes is:
Two walls (two vertical planes) meeting in a corner of a room that has a floor (horizontal plane)... most rooms have walls and floors, right?... my goodness, math is EVERYWHERE!! Is there a point (or points) that all three planes have in common? Do they "form" (your word) a point or do they _______________ (you fill-in-the-blank) in a point.
In the vernacular, what point or points do these planes share in common?
3d drawings can be a little tricky, but I will expect you to handle two walls and a floor. We'll work on it in class!
Hardy-har-har... I just crack myself up sometimes!!
A plane can be identified by any three points in the plane. Since we have learned that ANY three non-collinear points in space can form a plane, you can call it Plane ABC or Plane XYZ.
If the three points ARE collinear, then you could draw an infinite number of planes thru a single line. This is why three collinear point do not SPECIFY a unique plane. To visualize this, imagine a piece of construction paper (a plane) with a straw (a line) running down the middle lengthwise. The paper could be spun around the straw 360 degrees and all three points on the straw (aka line) would always be on the plane. The different locations of the paper represent different planes. We can discuss and demo more in class if that helps.
Picture vertical planes as vertical sheets of paper spinning around a pole or straw... almost in a "drill-like" fashion. If you can't picture it, we'll demonstrate tomorrow in class.
As for the three planes intersecting in a point... picture two walls (forming a corner) and a floor... where is their common point?
Vertical planes CAN intersect in a (vertical) line, but they CAN ALSO be parallel... visualize books standing next to each other on a shelf. Extend each book forever in any direction (on plane) and they will never intersect with one another.
How do you draw three planes to form a point?
ReplyDeleteGood question!! Well, one way to visualize three planes is:
ReplyDeleteTwo walls (two vertical planes) meeting in a corner of a room that has a floor (horizontal plane)... most rooms have walls and floors, right?... my goodness, math is EVERYWHERE!! Is there a point (or points) that all three planes have in common? Do they "form" (your word) a point or do they _______________ (you fill-in-the-blank) in a point.
In the vernacular, what point or points do these planes share in common?
3d drawings can be a little tricky, but I will expect you to handle two walls and a floor. We'll work on it in class!
Mr. C.
what do you call a plane when it is not labled?
ReplyDelete-Michael
a blue jet?
ReplyDeleteHardy-har-har... I just crack myself up sometimes!!
A plane can be identified by any three points in the plane. Since we have learned that ANY three non-collinear points in space can form a plane, you can call it Plane ABC or Plane XYZ.
If the three points ARE collinear, then you could draw an infinite number of planes thru a single line. This is why three collinear point do not SPECIFY a unique plane. To visualize this, imagine a piece of construction paper (a plane) with a straw (a line) running down the middle lengthwise. The paper could be spun around the straw 360 degrees and all three points on the straw (aka line) would always be on the plane. The different locations of the paper represent different planes. We can discuss and demo more in class if that helps.
Mr. C.
Also, how can 3 vertical lines intersect? Wouldn't that form just one line?
ReplyDelete-David
apparently one of my posts didn't get through- How can 2 vertical planes intersect?
ReplyDeletewhen the plane is diagonal is it horizontal or vertical?
ReplyDeletein number 34 I was kind of confused because I don't really know how three planes can intersect at one point without totally overlapping...
ReplyDeletePicture vertical planes as vertical sheets of paper spinning around a pole or straw... almost in a "drill-like" fashion. If you can't picture it, we'll demonstrate tomorrow in class.
ReplyDeleteAs for the three planes intersecting in a point... picture two walls (forming a corner) and a floor... where is their common point?
can a plane be a non expanding one like a line segment or are they all expanding for ever like a line
ReplyDelete-Jordan
How are we supposed to define the planes that are not labeled in the diagram?
ReplyDeleteDo the vertical planes have to have a vertical line?
ReplyDeleteVertical planes CAN intersect in a (vertical) line, but they CAN ALSO be parallel... visualize books standing next to each other on a shelf. Extend each book forever in any direction (on plane) and they will never intersect with one another.
ReplyDeleteHow should I name different planes?
ReplyDelete-Frank