All Questions
Tagged with triangles linear-algebra
81
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Understanding the geometry behind finding the area of a triangle defined by three vertices in three space
I am self-studying linear algebra using Jim Hefferon's Linear Algebra textbook (published in 2020). As I was making my way through the determinants section, I stumbled upon the following question:
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- 155
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Find the co-ordinates of a 3D triangle $ABC$ given 2 unit vectors, a side and a property
There is a triangle $ABC$ in 3D space. I am given the following:
$\vec{u}_{AC}:$ The unit vector along the direction of $AC$.
$\vec{u}_{BC}:$ The unit vector along the direction of $BC$.
point $A$ ...
- 105
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3
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Find all inscribed ellipses in a given triangle passing through two given internal points
Given a triangle, and two points inside it, I want to determine all the ellipses that are inscribed in the triangle and passing through both of the two given points.
My attempt: is outlined in my ...
- 24.5k
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What is the formula for the parameters of an ellipse based on the linear transformation of a triangle containing it?
Let:
$T_0$ be a $d$-dimensional triangle ($d \ge 2$) whose incenter is the origin and whose sides have known lengths $a_0$, $b_0$, and $c_0$; the corners of $T_0$ are $\vec{A}_0$, $\vec{B}_0$, and $\...
- 294
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Oriented area of a spherical triangle?
I want to know if there is a way to switch between the inner and outer areas of a sphere triangle based on the orientation of the vectors that make it.
For example let's see this picture:
If $A$ is ...
- 3,439
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24
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Angle within a rectangular-based prism
I've tried to find solutions to similar problems to see how this question should be solved but I didn't have much luck.
A rectangular-based prism is shown below. I need to determine the size of angle ...
- 1
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129
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Is it possible to have a scalar and vector part for an equation
Question: The median AD of the $\bigtriangleup$ABC is bisected at E, BE meets AC in F, then AF: AC is equal to.
Answer: The correct option is $\textbf{A} \frac{1}{3}$.
Taking A as the origin let the ...
- 1
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27
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Finding a mid-angle line between many points
For any 3 non-colinear points in 3d space (A, B, and Z) there should exist a line/vector M that connects Z to AB where AZM = MZB.
I am trying to find a corresponding M for a model with 5 points where ...
- 111
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2
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Proving that togling the direction of a polytope triangle yields the empty set
A triangle in the plane can be defined as the intersection of three half planes, each defined by the line passing through one of the segments and a normal direction pointing towards the interior of ...
- 3,439
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126
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How to find the x value that makes the vertices create a right triangle?
Essentially, there are 3 points $A=(10, −2, −10)$, $B=(20, −6, 0)$, and $C=(x, −2, −9)$ and I'm trying to find what value of $x$ makes ABC a right triangle. The issue is I don't really know how to ...
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Moving triangle along median of another triangle [closed]
For any given triangle and x value if I keep translating the two purple vectors down along the median, will they eventually both intersect A and B at the same time?
- 111
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94
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Angle preserving property by rotation seems to be violated in desmos plot
This plot I made in desmos has the vectors $v_1=[9 \quad 0]^T$ and $v_2=[9\quad 1]^T$. If we connect the two vectors, then we can form a right triangle, where the right angle is at the point $(9,0)$ (...
- 700
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Relation between the area of the four sections inside a parallelogram determined by four vertices and a random point inside it.
To note: There is a question on site with same diagram but the questions I ask regarding this diagram , are different.
Find $ S1$ in the parallelogram below
The Question:
Given:
$S_1 = 10\ \mathrm{ m^...
- 742
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2
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808
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Determinant formula for coordinates of circumcenter and orthocenter of a triangle
I've come across the following formulas for coordinates of circumcenter $O=(x_O,y_O)$ and orthocenter $H=(x_H,y_H)$ of a triangle, in a formula book, stated without derivation. For a triangle with ...
- 3,868
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416
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uniqueness of barycentric coordinates of a simplex
Let $k,d\in\mathbb N$, $p_0,\ldots,p_k\in\mathbb R^d$ be affinely independent and $$\Delta:=\left\{\sum_{i=0}^k\lambda_ip_i:\lambda_0,\ldots,\lambda_k\ge0\text{ and }\sum_{i=0}^k\lambda_i=1\right\}.$$
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