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.

1925 questions
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Points and a tangent plane

The task is: "Find the point(s) on $x^2+y^2+z^2 = 8$, where the tangent plane is parallel to the plane $x-y+2z=0$" What I did is: $f(x,y,z) = x^2+y^2+z^2-8$ grad$f = (2x,2y,2z)$ normal vector of $x-y+2z=0$ is $n=(1,-1,2)$ grad$f \parallel n \iff…
Roxell
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Equation of plane given a point and contain line of intersection of 2 plane

What is the equation of the plane that passes through the point $(−1, 2, 1)$ and contains the line of intersection of the planes $x + y − z = 2$ and $2x − y + 3z = 1$? How can i find the equation of the plane?
Yixiang Guice
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An elementary geometry problem involving two circles and tangent lines

From point C the two tangent lines' touch points with circle k1 are A and B. Circle k2 touches the AB line at B(so if O2 is the centre f k2, then O2BA∠=90°), and C is on k2 too. The other crosspoint of the two circles is M. Prove that the AM line…
ILikeMaths
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Is it possible for two non parallel planes to not intersect with each other in 3d?

I read that two lines in 2d if they are not parallel they will always intersect but in 3d it is possible for two non parallel lines to not intersect but what about the planes , is it possible two non parallel planes in 3d to not intersect with each…
Endrit Shabani
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Is it the same when it says to write an equation of plane that contains two points and is determined by two points?

All those plane equations are confusing me so much Is it the same when it says to write an equation of plane that contains two points and, is determined by two points ? (I am assuming that a vector is given aswell , because I think its not possible…
Johnny Adams
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Isoceles Triangle inscribed in Rectangle

So I have rectangle $ABCD$ with isoceles triangle $EFC$ inscribed inside it. I know the angle $\angle ECF$ and the length of $FB$ and $FC$. Is there some way to find $EA$ and $FA$? My intuition says yes, but after bashing at this problem for 30…
JSCoder says Reinstate Monica
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Planes that are parallel to axis.

If a plane is parallel to the $x$ axis then it's perpendicular to the $YZ$ plane. That's what my book is saying but I have a question. If a plane is parallel to the $X$ axis then shouldn't it be also in parallel to the $Y$ axis thus it's also…
user8700093
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Find a matrix representing linear transformations

I've been asked to find a matrix representing projection of a point in the plane onto the line $ax + by = 0.$ I know the matrix for $ax+by$ is $$\left[\begin{array}{cc}a &0\\ b&0\end{array}\right]$$ I also know projection of $u$ onto $v$ is…
user491575
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Estimating a location of point C on a map based on the change in distance from AC to BC using the respective radii around point A and B

I was just wondering, suppose your current location is A and you know a point C is ym away, if you know move to point B and B is consequently only xm away from C, (given ym>xm) could you approximate the location of C using two radii?
Liamedwards
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High school Geometry

Let ABCD be a trapezium. AB is parallel CD. EF is a line parallel to AB and CD. E is on BC. F is on AD. What is the length of EF in termsof sides of trapezium? Given AC/CD=M/N=BF/FC. I derived the answer for special case in which the line joins…
Vindhyachal Vindhyachal
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A question in plane geometry.

$A,B$ are two fixed points in a plane. Given any third point $P$, can we always find a point $O$ such that either $\overline{OA}<\overline{OP}<\overline{OB}$ or $\overline{OB}<\overline{OP}<\overline{OA}$? PS : I've asked many questions in this…
Rajesh D
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Planes and their equations

In the last part of the question, an equation of a plane is provided. Can the equation $r=pi+qj$ correspond to a 3D-plane? What are its direction vectors? In my opinion it only has only one direction vector $(0,0,1)$ (this is actually used in the…
mathnoob123
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Ratio of Radii of two circles

The question is this " Inside a circle of unit radius, an angle of $60$ is formed by the minor arc. A circle is drawn touching the two arms of the chords $PA$ and $PB$ and also the bigger circle tangentially. Find the ratio of the radius of the two…
Jyotishraj Thoudam
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Finding a plane rotation and angle

My question may be simple compared to some of the questions I see here but it has me stumped. I have a 3"disc with an X, Y, Z origin at the center. X and Y form the plane of the disc and Z extends vertically. I rotate 10° about the X-axis, 20° about…
Alex
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Finding the equation of a plane that passes through the line of intersection of 2 planes and forms a 45 degree angle with another plane.

How to find the equation of the plane that passes through the line of intersection of the planes $x+5y+z=0$ and $x-z+4=0$, and that forms a 45 degree angle with the plane $x-4y-8z+12=0$?
user391135
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