What is the intersection of two planes called?
If they are not parallel, it is called a line. If they are parallel (ie identical normal vectors), then if the planes are identical (ie distance between =0), then the intersection is the plane itself (a plane) else it does not intersect.
Can two planes intersect in a line segment?
yes. planes can be finite, infinite or semi infinite and the intersection gives us line segment, ray, line in each case respectively. if two finite planes intersect each other we obtain a line segment.
There are 10 lines in a plane, each intersecting each other. No three lines pass through the same point.?
Intersections are 45. Each line is intersected by 9 others so it has 9 intersection points on it. 10 lines * 9 points on each equals 90, but you have to divide by 2 because each intersection is bisected by two lines. The other trickier. I think the answer is 2+2+3+4+5+6+7+8+9+10 or 56 but I could be wrong. My idea is that the first line splits the plane into 2 parts, the second, 2 more parts, the third adds 3 more, and the 4th line 4 more, etc.
Find the point (if it exists) at which the following planes and lines intersect.?
That line will intersect the plane z = 4 where the z-coordinate is equal to 4. As the z coordinate is parametrically defined to be t - 6, it will intersect z = 4 where t - 6 = 4, so t = 10. Subbing t = 10 into 2t + 1 gives an x-coordinate of 21 and similarly the y coordinate will be obtained by subbing t = 10 into -t + 4 to get -6. So the point is (21, -6, 4).
List all the possible intersections of a line and a square in a plane?
A ....... ------- ---------- ........ B ...........| .. . . . . . . . . . | ...........| .. . . . . . . . . . | ...........|a. . . . . . . . . . | ...........| .. . . . . . . . . . | ...........|x----b-- ------- | ....... .... .. ... ...C ..... .. ......D . . . E Let various lines pass through point A. I can't draw the actual lines, so use your imagination on these: Line AB intersects the square in a line segment (along the top of the square) Line AC intesects the square in 2 points (a and b) Line AD intersects the square in 1 point (the corner x) Line AE 'intersects' the square in 0 points - missing it entirely. No finite set of 3 or more points lies on a line which intersects the square.
Can two planes intersect in a single point?
The reason they can not is that the planes are endless. If they were finite planes, say like a piece of paper, you could make the corner of one paper touch the other. But you have to imagine they are like never ending pieces of paper, lol. So there is no corner. Anyway you picture them, there is going to be a never ending line where they intersect. I think if I had to draw that, I would look in a math book or online to see a sketch. I can't really draw it here. Can you picture it, though?
Can two parallel lines intersect?
In normal geometry and planes, saying that parallel lines meet at infinity is wrong.Reason: take two lines X=2 and X=3 in a plane, no matter what, they will never meet as there will be a distance of one unit in between them.However, you can construct other forms of geometry, so-called non-Euclidean geometries. For example, you can take the usual points of the plane and attach to them an additional point called "infinity" and consider all lines to also include this additional point. In this context, there is a single "infinity" location where all lines meet. In a geometry like this, all lines intersect at infinity, in addition to any finite point where they might happen to meet.Now suppose, we are given two lines that are almost parallel. i.e. consider the part of geometry in consideration to be origin, and these two lines appear to be parallel, but have a slight inclination towards each other. Suppose the point where they meet, the angle of intersection is 0.00000000005 degrees, they surely will not intersect for a long distance and hence, the lines are considered parallel (Since they are almost parallel and the calculations on this minor factor wouldn't cause change in results. Also it would make the calculations easier).Source: Do Parallel Lines Meet At Infinity?
If 2 Lines Never Intersect Do They Have to be Parallel?
If you are on a 2 dimensional plane, then it is easy to show that any linear curves i.e. lines that aren't parallel intersect and also that the solution set to where two parallel lines intersect is the empty set. So to Answer your question, if they don't intersect then yes they are parallel. Proving the first statement effectively proves what you are after. If you have lines y = m1 x + c1, y = m2 x + c2. Now the point of intersection is where these equations match, i.e. m1 x + c1 = m2 x + c2 x = (c2 - c1)/(m1 - m2) so x has a finite solution as long as m1-m2<>0 => ,m1<>m2 by finite solution I mean intersection also it is noteworthy that two lines being parallel implies that m1 = m2 and therefore there is no finite intersection point. If you are on an n-dimensional plane with n>2 then they dont have to be parallel. Also note that 2 n-1 dimensional lines must be parallel to not intersect, i.e. 2-d planes in 3-d intersect unless they are parallel.