2
votes
If we spin an ostrich egg along its minor axis will it be oblate shape?
Forget about spinning. An ellipsoid has three perpendicular axes; it can be constructed from a sphere, by stretching it along these axes. The stretch factors may or may not be equal.
It's called a ...
- 5,726
2
votes
Accepted
Perpendiculars in 3 dimensions
I agree that it seems slightly easier to prove that $CB$ is perpendicular to the first instantiation of $\mathbf w$ than to prove that $UA \parallel CB$.
Once you have done that, from the fact that ...
- 100k
2
votes
Accepted
Locus of a point whose distance from two points is fixed (but not necessarily equal) in 3D geometry
Just to give you an answer:
Indeed if $d(P,S_1)$ is constant, then $P$ lies on the spherical surface $\odot(S_1,S_1P)$, on the same manner $P \in \odot (S_2,S_2P)$. Because $P$ is on the meeting of ...
- 1,940
1
vote
Accepted
How to "Clamp" one unit vector between two others?
This might be a lot more irregular than you expected, but there's not going to be a simple clean formula. Expect a lot of if statements if you're coding this.
Okay, ...
- 11.2k
1
vote
Finding equation of line of intersection of two planes
You assumed tacitely that $n_1,n_2$ are linearly independent, i.e.
$$\|n_1\|^2\|n_2\|^2-(n_1\cdot n_2)^2>0.$$
I leave it to you to solve the Cramer system
$$(a n_1+bn_2)\cdot n_1=(a n_1+bn_2)\cdot ...
- 39.7k
1
vote
Why is the vector making equal angle with 3 non zero non-coplanar vectors [a,b&c] is not along Σa[unit vector]
Given three unit vectors $a,b,c$. The vector $v$ that is equiangular from these three vectors must be on the bisecting plane of $a$ and $b$. Also it is must be on the bisecting plane of $b$ and $c$, ...
- 24.5k
1
vote
Heesch numbers in 3D
While experimenting with 3D tilings, I came up with these solids, which have Heesch numbers one, two, and three. There is also this example by Jadie Adams et al. http://web.archive.org/web/...
- 11
1
vote
Sphere with smallest radius
A direction vector of Line1 is $u_1=\langle2,-1,-1\rangle$.
A direction vector of Line 2 is $u_2=\langle-3,-6,4\rangle$.
A directon vector of the smallest distance $P_1P_2$, introduced by Satish ...
- 11.9k
1
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Sphere with smallest radius
The first line is given by
$P_1(t) = (5, 2, 5) + t ( 2,-1,-1) $
And the second line is given by
$ P_2(s) = (-4, -5, 4) + s (-3, -6, 4) $
Define the squared distance function as follows
$ f(t, s) = (...
- 24.5k
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