Mathematics Stack Exchange
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Questions tagged [3d]

For things related to 3 dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For non-planar geometry, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

This tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead . For non-planar geometry, but otherwise agnostic of dimensions, perhaps or should also be considered.

Learn more about 3-dimensional space here.

3724 questions
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Rotation of plane along a line

The plabe $x+2y+3z=7$ is rotated about the line where it cut yz plane by an angle m . In the new position the plane contains the point (-1,0,2) . We have to find cos m. My try Equation of yz plane is x=0 equation of rotated plane would be…
Koolman
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Variable volume of tetrahedron

Let the 5 sides of terahedron be 1 . And the sixth side is x . Now how can we comment that how the volume of tetrahedron with varying x . When it gets maxima .
Koolman
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How do you calculate the volume of a $3D$ parallelepiped?

Find the volume of the parallelepiped with vertices $(0,0,0)$, $(3,0,0)$, $(0,5,1)$, $(3,5,1)$, $(2,0,5)$, $(5,0,5)$, $(2,5,6)$, and $(5,5,6)$. When in $2D$, I usually rely on the Shoelace Formula to solve these types of questions. How do you do…
user406996
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Word for three-dimensional cevian

Is there a specific word for three dimensional cevians? I am referring to the line segment from a vertex of a tetrahedron to the opposite face. I have tried looking this up but have not found any results.
Fermat
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Finding value of $t$ such that volume contained inside the planes is minimum

The question is to find out the value of $t$ such that volume contained inside the planes $$\sqrt{1-t^2}x+tz=2\sqrt{1-t^2},$$$$z=0,$$$$x=2+\frac{t\sqrt{4t^2-5t+2}}{\sqrt{12}(1-t^2)^{1/4}} \text{ and }$$ $$|y|=2$$ is maximum. I tried to figure out…
Navin
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Then minimum value of $PX+PY$, where P is a point on the plane

If $X(1,1,1)$ and $Y(2,2,4)$ are two fixed points for $P$ be a variable point in line $2x+y+z=1$. Then minimum value of $PX+PY.$ Attempt : points $X(1,1,1)$ and $Y(2,2,4)$ are lie on sime side of plane $2x+y+z = 1$ wan,t be able to go further ,…
DXT
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Image of plane with respect to plane

Find the image of plane $2x – y + z = 2$ in the plane mirror $x + 2y – z = 3$. Could someone give the concept to find the image plane in shortest way possible. One way which I think is that if we take $P_1:2x – y + z = 2$ and $P_2: x + 2y – z = 3$,…
user383014
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Need to get 3D coordinates from 2 degree variables on sphere

this is kind of an odd one, and I'm not quite sure I'm asking at the right place, but here is goes: let's say you have the following: (assuming everything is based around the point of origin) You have a degree of a circle ex: 90, and a radius, you…
Creeper9207
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Parrallelogram with given ratio

Points $X$ and $Y$ are taken on the sides $QR$ and $RS$, respectively of a parallelogram $PQRS$, so that $\vec QX:\vec XR =4:1$ and $\vec RY :\vec YS=4:1$ . The line $XY$ cuts the line $PR$ at $Z$ we have to prove $PZ=(21/25)PR$. I am not getting…
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
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Show that the points are collinear

Show that the points $$\mathbf a-2\mathbf b+3\mathbf c ,\quad 2\mathbf a+3\mathbf b-4\mathbf c ,\quad-7\mathbf b+10\mathbf c$$ are collinear. Where $\mathbf a ,\mathbf b,\mathbf c$ are vectors . I thought as Let the points be $k ,l ,m$…
Koolman
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coplanar lines in 3d plane

If we are given two lines Coplaner then how can we find the value of k. I think if they are coplaner then their cross product should be zero . In the solution it is given as But I could not understand what they have done.
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
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Number of Planes in 3-D unit distance away from three given non-collinear points are?

Number of Planes in 3-Dimensional geometry unit distance away from points $A(3,5,1)$, $B(-3,-5,1)$, $C(10,-2,5)$ is ? I have easily counted two such planes $P_1,P_2$ which are parallel to the plane($P_3$)containing the three points lying on…
Freelancer
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Equation of a plane contains a line

How can we write equation of a plane which contains a line l$_1$ and is parrallel to another line l$_2$ . I am not getting start , how to do it . Please help me
J.Doe
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Mapping a disk to a point in 3D

I have been told that a disk with center (a,b) and radius r can be mapped to 3D point. And the 3D point is $(a,b,a^2+b^2-r^2)$. However i do not know what is the idea behind it. How do you calculate this point and how do you prove it? Inversely if…
kotoll
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Find dot in the middle of the cube?

I have several cubes, those cubes have the 8 vertices, for example: Vet X Y Z ----- CUBE1 ----- (top side) V1: -0.5 0.5 0.5 V2: 0.5 0.5 0.5 V3: 0.5 0.5 -0.5 V4: -0.5 0.5 -0.5 (bottom side) V5: -0.5 -0.5 0.5 V6: 0.5 -0.5 0.5 V7: …
Leonardo
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