intersecting lines.
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Non-coplanar lines. They could be parallel or skew.For example, consider yourself facing a wall in a cuboid room. Line 1 = where the floor meets the wall in front of you, Line 2 = where the ceiling meets the wall in front of you, Line 3 = where the floor meets the wall behind you. Then Lines 1, 2 and 3 are parallel but not in the same plane.OrLine 4 = where the walls to the left and behind you meet. Lines 1 and 4 are not parallel nor in the same plane: they are skew.
Not necessarily. Two skew lines will not lie in the same plane. For example, consider you are standing in a cuboid room facing a wall. Then think of line 1 = the line where the floor and opposite wall meet. Line 2 = the line where two other walls meet. These two lines are not in the same plane.
Assuming that by opersit is meant opposite, the answer is NONPARALLEL LINES. If they are in the same plane then (and only then) they would be intersecting lines (lines that meet at some point in the plane). But if they are not in the same plane they need not meet even if they are not parallel. So the answer that they are intersecting lines is incomplete and therefore incorrect. To visualise nonparallel lines that do not intersect, consider a room. Think of the [horizontal] line formed by the floor and the wall opposite you. Think of the [vertical] line formed by the wall behind you and the wall to your right. These two lines are not parallel, but they will not meet - ever.
They are simply non-concurrent lines. They need not be parallel. To illustrate that consider yourself in a cuboid room standing with your back to one wall. Line 1 is where the floor and wall meet behind you. Line 2 is where the left wall meets the wall facing you (the far wall). The two lines do not intersect but they are not parallel. There are many other such lines in the room.
Determine how large of a 45 degree angle you wish to have where your walls meet your ceiling. Cut an appropriate number of 2x4s with a 45 degree angle on both sides all the same length. Its nice if you can place these 16" on center, but 2' on center is acceptable. Hold one in place at each corner of the room and make pencil line on the wall at the bottom tip of the 2x4. Snap a chalk line on the wall between the pencil lines. You can do the same thing on the ceiling if you wish. follow these lines and you'll wind up with a straight ceiling. Make sure you attatch these 2x4s straight up and down to a wall stud and the corrusponding ceiling joist or truss. It gets complicated when you get to a corner. You need to establish a " ridge beam" from the chalk lines that meet in the corner on the wall to your 2x4s that meet on the ceiling. this will require 4 compound miter cuts. comtinue running the 2x4s on layout into the corner but instead, connect them from the wall to the newly established "ridge beam" these will also require a compound miter on one end. Then have a sheet rock party. If the corners sound too intimidating, do every thing else and call in a pro to finish the corners. at least you'll save money anyway. Make sure the pro is aware of your plan on how you're going to install the tray ceiling before you begin, he may have additional bracing or a different way all together. Hate to have all your work wasted. Hope this gives you somewhat of an idea