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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How do I align these letters to the same baseline?

Given the following letters, all are absolutely aligned vertically to the bottom, however I need to align them to their baseline. How can that calculate the letter vertical offset? Each letter is currently displayed vertically with y = bottomY -…
Yanick Rochon
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Plane equations

Please advise on a suitable method. Thanks in advance! Question: The planes m and n have equations 3x+y-2z=10 & x-2y+2z=5 respectively. The line L has equation r=4i+2j+k+(lamda)(i+j+2k). i) Show that L is parallel to m. ii) Calculate the acute angle…
Manon Blackbeak
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What is the vector equation for the line of intersection of two planes with the only given information being their distances from the origin?

The question I'm working on is: Two planes have non-parallel unit normals n and m and their closest distances from the origin are 3 and 7 respectively. Find the vector equation of their line of intersection. I have calculated the implicit vector…
Jbo
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How do I find the equations of the planes containing the faces of this tetrahedron?

The points are $(0,0,2), (0,2,0), (0,0,0),$ and $(4,2,0)$. I know the y and z components of the equation will just be the intercepts but I'm not sure how to incorporate the $(4,2,0)$ point. I need the equations to calculate the flux using the…
HokieFan7
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Most compact representation of a plane

A common way to represent a plane is: $$ a x + by + cz +d = 0 $$ Where (a, b, c) is the normal vector and corresponds to the orientation of the plane and $d$ is the distance from the origin following the normal direction. This would define the…
Leonardo Mariga
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Need to find the angle between two planes

Lets say, the rings A & B are on top of each other, I say there are completely ordered. If they are side by side (Like both rings on a same plane), then I say they aren't ordered at all. If I just calculate the angle between the normals, then In…
Adupa Vasista
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The equation $r = 3\cos(\theta)$ in polar coordinates describes a line in the plane. True or false?

Just as the title describes. Is it true or false? I know it is a line in 2D, but circle in 3D.
bingobongo
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Plane Fitting, why everbody set c = 1?

I want to fit a plane which has the following equation: $ax+by+cz+d=0$ Having a overdetermined system (more than 3 points), most people solve that equation using the normal equations (Least square). Because most people minimize over $z$-Direction,…
horsti
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Check collinearity in 3D if points are noisy

Can anybody tell me how I can check collinearity in $\mathbb{R}³$ ? I have multiple points, which I need to check for collinearity. According to wiki, I can do this by looking at the rank of a matrix (if I write those points into the matrix…
horsti
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Can you find the normal vector to the plane by dot product instead of using the cross product?

I am trying to calculate the normal vector of a given plane with dot products on the one hand(Attempt 1) and with vector cross products on the other (Attempt 2). The results aren't making any sense to me: shouldn't both attempts which result in…
user764281
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How to simplify this dot expression.

I feel I have a fair understanding of the vector equation of a plane, however I am stumbling on manipulating the following equation to t: Equation Post I need assistance in understanding how the author simplified the plane equation to the solution…
user764281
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Launching a particle to reflect off of the interior of a circle in exactly eight distinct points

This question was recently asked on a National level Olympiad. It reads: Consider a circle of radius $R$ centered at the origin. A particle is launched from the $x$-axis at a distance $d$ from the origin such that $0
SuyN
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Two planes intersection line may not be straight?

I have two planes $$2x+3-z=0$$ $$5y+xz=0$$ The intersection line of this planes can be found by solving the system above for $x$ and $y$, expressed by $z$(or $y$ and $z$ expressed by $x$). The result is $$y=-\dfrac{1}{5}x(2x+3)$$ $$z= (2x+3)$$ Now…
Stdugnd4ikbd
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Understanding the equation of plane

I have a simple question regarding plane (sorry, if it may sound incorrect, I am confused to understand it). In general, plane is a two-dimensional surface that extends infinitely far. If it is two-dimensional surface, then each point in the surface…
ssane
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Convert plane from ax+by+c=z form to ax+by+cz+d=0 form

How to I convert a plane from the ax+by+c=z form to ax+by+cz+d=0 form?
user1436508
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