Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [plane-geometry]

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded in a 2D plane.

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded in a 2D plane.

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The change in the $~y~$-coordinates when a plane is inclined, the coordinates are cartesian

I have a plane of size wxh. Its a horizental plane (with $~x~$-axis the angle is zero). I incline it with the angle alpha. How would I calculate the $~y~$-coordinates? I suppose that the $~y~$-coordinates remain the same. Thanks Shan
Shan
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If the opposite angles of inscribed quadrilateral are always supplementary, where did I lose the train of thoughts in this example?

I embedded this diagram to make easier the understanding of my question. Starting with the quadrilateral ABCD, the central angle ABC that subtends the arch formed by the inscribed angle X, according to the “Inscribed Angle Theorem”, should be…
igortp
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Find a general form of a subplane

I am trying to find a general form of a subplane $ x=2+5t$ , $ y=3$, $ t \in \mathbb{R}$.I know how to find a general form of a line, but not a plane. Could you help me? Thanks!
J. Doe
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Calculating the velocity of a particle on a spinning disc

The particle is moving towards the center as the disc is spinning, the position of the particle is described by the following expression: $r = r(t) cos(ωt)i + r(t) sin(ωt)j$ How do I calculate the particles velocity?(not angular velocity)
noname197
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1.a) A plane $S_{1}$ contains the three points $(1,0,0),(0,1,0)$ and $(0,0,1) .$ Find an equation for $S_{1}$

1.a) A plane $S_{1}$ contains the three points $(1,0,0),(0,1,0)$ and $(0,0,1) .$ Find an equation for $S_{1}$ 1b) The perpendicular from the origin $\mathrm{O}$ to another plane, $\mathrm{S}_{2}$ meets it at $(1,1,0) .$ Find an equation for…
Tariro Manyika
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Detect Crossed Paths on a Plane Given Coordinates.

If you have the $X$ and $Y$ coordinates for $2$ lines on a $2D$ plane/graph is it possible to detect via true/false if they cross paths? I'm just trying to detect if lines are not parrallell. If $(X,Y)$ is $(20, 20)$ to $(X_2,Y_2)$ of $(30,30)$…
DaveyBoy85
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Finding the angle between a line and plane exercise

The aim is to find the angle between a line and plane and if they intersect then the point where they do that. given: $$ \frac{x+1}{2}=\frac{y-3}{4}=\frac{z}{3}, 3x-3y+2z-5=0 $$ What I have found out: s=(2; 4; 3) n=(3; -3; 2)…
Student123
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Vector addition exercise: Plane and Wind

I sit since 2 days on it and can't solce it: A plane flies with the speed of vF=240 km/h in direction of north. It flies into a storm from north east with the wind speed of v=90 km/h. What's the actual speed of the plane above the ground and how big…
Flo
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Length and perimeter

Hello guys? I have been having constant disagreements with my fellow professors on this question. A field was to be fenced using 816 posts placed 4 meters apart,leaving a 4 meter space for the gate.If 3 strands of wire were used ,what would be the…
Makau Elijah
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Line and distance equation

I've studied line geometry especially one that has to do with distance formula and question. But I just don't know how to approach this question Find the equation for the set of all points equidistant from the line y = 1 and the point…
Michael Umande
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Meaning of $a^2 + b^2 + c^2 = 1$ in a normal form plane equation

As stated above. I know that the $a, b, c$ represent the normal vector of the plane and that you can normalize them so that $a^2 + b^2 + c^2 = 1$. But what is the main reason for doing the normalization?
Taylor
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Given the angle between planes $\pi_1$ and $\pi_2$ is equal to the angle between...

I'm not sure where I'm going wrong with this question but i keep coming to a hexic equation rather than a quartic equation. the three planes: $$\pi_1: ax+2y+z=3$$ $$\pi_2: x+ay+z=4$$ $$\pi_3: x+y+az=5$$ Given the angle between planes $\pi_1$ and…
H.Linkhorn
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parallel lines and a plane

Explain why two parallel lines define a plane. If I hold two pencils so that they’re parallel, there’s only one position in which a plane can rest on both pencils.But can someone give me a more valid reason? Should I use definition of a plane?
Donna
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Equation of Plane through Center

I have a pentagon for which 3 vertices were chosen to compute the equation of the plane. How to I find the normal passing through its center? $$P_1 = [ 3.096, \ 0.492, \ 3.287]$$ $$P_2 = [ 3.118, \ 0.227, \ 4.669]$$ $$P_3 = [ 2.214, \ 1.476, \…
EA00
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Single Point in other Dimensions

Would a single point and a fixed distance determine a unique segment in 2-space or 3-space like it does in 1-space when given the length of the segment and location of its midpoint? Please explain your answer. I think it would be a unique segment in…
Donna
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