Does anyone understand coordinate planes?If so can you put it in words?
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This is a method like grid squares on a map so you can specify a point relative to a known origin by x distance right and y distance up. \nIf three planes are used you can also specify a point in 3D space so that if you lay your sheet of paper flat with x and y marked, the z distance is above the paper, like height of a mountain above a flat map.\nLeft and down are given negative values.\nAs well as defining single points, you could specify shapes according to how the distance in the y direction relates to the x distance.\nSo x = y (often more confusingly written as x-y = 0 ) defines a line connecting points (x,y) such as (1,1) (2,2) (5,5) (1000,1000) at 45 degrees between the x and y axes.\nAlso, more advanced, X cubed + y cubed + z cubed = 27 is a sphere, centred on O with a radius of 3
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#1\n\nThe normal to the plane 3x - y + z = 1 is <3, -1, 1> (the coefficients of the variables).\n\nThe line with the same direction as this vector through the point (8, 4, 0) can be defined by the parametric equations:\n\nx = 3t + 8\ny = -t + 4\nz = t\n\n(The coeffiecients for t are that of the vector and the constants are from the point.)\n\nNow to find where the line intersects the coordinate planes, set x, then y, then z as 0.\n\nyz-plane: x = 0\n0 = 3t + 8\nt = -8/3\nSo y = 8/3 + 4 = 20/3\nz = -8/3\n**The point is (0, 20/3, -8/3)\n\nxz-plane: y = 0\n0 = -t + 4\nt = 4\nSo x = 12 + 8 = 20\nz = 4\n**The point is (20, 0, 8)\n\nxy-plane: z = 0\n**This is the given point (8, 4, 0)\n\n\n#2\n\nThe first line contains the vector <1, 6, 2> and the point (2, 2, 2).  The second contains the vector <3, 21, 8> and the point (2, 3, -4).\n\nThe vector between the two points is <2-2, 2-3, 2--4> = <0, -1, 6>.  You can project this vector onto one of the lines.\n\nRemember that the length of the projection of vector b on vector a is equal to the dot product of a and b over the magnitude of a.\n\nIn this case vector b is between the lines and is <0, -1, 6> and vector a is one of the lines; I'll pick line 1 and vector <1, 6, 2>.\n\na dot b = 0*1 + -1*6 + 6*2 = -6 + 12 = 6\n\nmegnitude of a = sqrt(1 + 36 + 4) = sqrt(41)\n\nTherefore, the magnitude of the projection is 6/sqrt(41)\n\nNow you have two sides of a right triangle.  The hypotenuse is so called vector b, so we need its magnitude.\n\nmagnitude of b = sqrt(0 + 1 + 36) = sqrt(37)\n\nNow just find the length of the final side - d, the distance between the skew lines!\n\nd^2 + 36/41 = 37\n\nThen just solve for d and you have your distance.\n\nI hope this helps!  Good luck with your final!\n\nP.S. I double-checked my math, but check it just is case I made a mistake and didn't catch it.
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there are three defined axes in coordinate system.\nx-axis\ny-axis\nz-axis\nalthough Einstein in the last days of his life started talking about fourth-axis.\nthat is still undefined.\nfor present,coordinate system,there are three axes only.
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"Cartesian coordinates come from his last name, Descarte."\n\nActually, you are only half right. The Cartesian plane comes from Descarte's Latin name, Cartesius, which is what he used when publishing his proofs. \n\nOnto the question at hand, I'm not even sure what you are asking. What did Rene Descartes use the first letters of? Grammatical abnormalities notwithstanding, this question is very vague. What exactly do you mean?
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e is the correct answer\n\ncoplaner means all in the same plane. the magnitude of the three can result in a, b, or c.\n\nd is impossible
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since your ddoing coordinate geometry you should at least tell what shape you're trying to get.\nI'm assuming it's a parallelogram so u should make it (1,8)
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You would be better off writing a story in your own words... but you first need to find a list of geometric terms.  Did you get one from your teacher or are you supposed to make up your own list?\n\nThink about shapes (squares, octagons, circles, etc.) and other geometric terms (line, ray, plane, angle, etc.) then find inventive ways to add them to your story such as "She and her *circle* of friends walked past the *octagonal* stop sign.  They saw a group of boys that they thought were all *squares* standing in a *line* to get tickets.  Through the clouds came a *ray* of sunshine as a *plane* flew over head.  Suddenly the jet entered a steep *angle* and began heading toward the ground..."\n\nYou get the idea.  This should be a fun activity, not a laborious task.  Enjoy yourself rather than having someone else get the fun.
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Let center point be [0 0] of a rectangular coordinates system.\nAssume the object’s face be initial position on the plane; that is X-axis goes from [0 0] to object’s face, let Y-axis be X-axis rotated through [0 0] by +90 degrees. This way we have defined a rectangular system of coordinates on the plane. \nLet x & y be coordinates of a random point p in our rectangular coordinates system. \nNow lets consider polar coordinates system. Trace vector V from [0 0] to p, then\nx=r*cos(a) & y=r*sin(a), a degrees being angle from X-axis to V, r=sqrt(x^2+y^2). \nAngular position a of p=[x y] should be found as following.  \nAs tan(a)=y/x, (or cotan(a)=x/y), then a=Arctan(y/x) is general solution. Angular position a could be found for any pair of [x y] but [0 0] or when r=0.\nWe do not need general solution in our problem. Our solution must be:\nLet b=arctan(|y/x|) degrees, then a=b for x>0 & y>0, being 0<=a<=90; a=-b for x>0 & y<0, being -90<=a<0; a=180-b for x<0 & y>0, being 90<a<=180; a=-180+b for x<0 & y<0, being –180<a<-90.\nThus the object must be rotated by an angle of abs(a) degrees determined above in the direction of sign(a). \nRotating in opposite direction means to rotate the object by an angle of (360-a) or (–360+a). abs(360-a)=abs(-360+a) is always greater than abs(a).
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They pass each other at 2:20pm.\n\nOne way to figure this out is by considering the problem on an x-y graph:\n  Think of the x-axis as elapsed time, in hours.  So for example, x=1 would be 1 elapsed hour (or 1:00pm).\n  Think of the y-axis as position, in kilometers.  So think of Austin as being y=0, and Los Angeles as y=2100.\n\nThen, consider the trip of the two planes as two lines (ie. y=mx+b) on this graph.  In the end, youll use these lines to solve the problem.\n\nOk... so the plane that starts in Austin would be y=500x.  The reason we know this is because:\n   1)  at noon (x=0), the plane is in Austin (y=0).\n   2)  if you look at the way we set up the graph, the speed of the plane happens to be the slope of the line (notice "km/hr" = y/x), so the slope is 500.\n\nThe plane that starts in LA is slightly more complicated.  Its y=(-700x)+2800.  We know this because:\n   1)  at 1PM (x=1), the plane is in LA (y=2100)\n   2)  its speed is 700km (but in the opposite direction), so its slope is -700.\n\nSo, we're looking for when the two planes intersect... They intersect when their positions (their y values) are equal.  So you just need to solve the two equations with their y=values as being equal.\n\ny = 500x\ny = (-700x)+2800\n\n500x = (-700x)+2800\nx = 7/3\n\nOk so x = 7/3... Remember that x is elapsed hours, so 7/3 = 2 1/3 elapsed hours = 2 hours and 20 minutes....  or 2:20PM!\n\nYou can verify this by plugging x=7/3 into both of the equations.   You'll get y=1166.667, which puts the planes right around New Mexico =).
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None of those are "planes".\n\nA plane is drawn as a square simply because of the limitations of a sheet of paper.\n\nA plane is infinite in two directions.  It has no start or end point on the xy axis.  A sheet of paper of course does have start end end points.  Usually 8x11\n\nNone of rectangels, squares, or triangles are planes.  They are all subsets of them.  And darned small ones at that.\n\n-Dio
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It's been too long for me.\n\nSample many definitions. Go to MATHWORLD.COM (lower case)\n2 geometric figures are CONGRUENT when one gets transformed into the other by isometry.\n\nStay with it.\n\nGRIZZ
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electrons can't line up in a plane they wouldn't all fit... unless it was like a big 747... or one of those military airbus things... and by 3d do you mean 2 spacial dimentions + time or 3 spacial dimensions? cause we already live with 3 spacial dmension (4 including time)
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I will take a shot at it.\n\nWe are all very familiar with 3 dimensional space, up down, left right, forward backward. To describe the location of an object in space we have to use those three dimensions. BUT. Nothing is actually fixed in space. Everything is moving. So in order to describe the location of an object in space you must also describe at what time that object was at that location or will be at that location. That is why time is called the 4th dimension. \n\nNow here is the really bizaar part. Some scientists think there are more than 4 dimensions. Some propose 10 dimensions and some 26 dimensions. It is called string theory and it is all over my head.
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the Cartesian coordinate system is develop used to uniquely determine each point in the plane through two numbers, usually called the x-coordinate and the y-coordinate of the point. To define the coordinates, two perpendicular directed lines (the x-axis or abscissa and the y-axis or ordinate), are specified, as well as the unit length, which is marked off on the two axes (see Figure 1). Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimensions.\nCartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. This work was influential in the development of analytic geometry, calculus, and cartography.\n\nThe idea of this system was developed in 1637 in two writings by Descartes. In part two of his Discourse on Method he introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as measuring guides. In La Géométrie, he further explores the above-mentioned concepts.
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They are called the X axis and the Y axis.\n\nThe position of any point on a grid can be described by a pair of numbers: its coordinates.\nThe first number, its x coordinate, measures its distance from the origin in the x direction. The second, its y coordinate, measures its distance from the origin in the y direction.
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(x,y) (-x,y)is a refelction over y axis. I think...
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hyperbolic plane, you can check what the different models for hyperbolic geometry are.\n\nanotherone, would be Riemannian geometry, which is the basis for relativity theory.\n`