0
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0answers
18 views

Solving ray/triangle intersection - comparison on methods

In 3D I have a ray $q + t\vec{d}$, and a triangle with vertices $a$,$b$,$c$. I want to find the parameter $t$. I have solved this by noting that a vector in the triangle plane is perpendicular to the ...
1
vote
3answers
37 views

Is this triangle question missing information?

In the $\Delta KLP$, find $a+b$: My question is that: isn't some information missing from the question? Because all I can see is is that $ \usepackage{ gensymb } \angle SKP = \angle LTS = ...
1
vote
0answers
144 views

Computing Euler Angles from Direction Cosines Vector

My problem simply as the following: Suppose we measured the orientation of a plane object with respect to a reference fame. (where the reference frame parallel to plane frame). The unit normal vector ...
0
votes
2answers
48 views

Question on inscribed equilateral triangle

Question: $ABC$ and $ODE$ are equilateral triangle with $BC || DE$. If $O$ is the center of the circle, then find the ratio $AQ:QC$ So, my thought on this is that, since we are not given the ...
2
votes
3answers
171 views

Find radius of a circle which is tangent to three known lines

I need to find the equation for a circle which is tangent to the following three lines: y=0 x=0 y=-x+0.338334 For the last tangent line equation, I know that it is tangent at the point (0.169167, ...
5
votes
1answer
86 views

Prove that $\|a\|+\|b\| + \|c\| + \|a+b+c\| \geq \|a+b\| + \|b+c\| + \|c +a\|$ in the plane.

Prove that $\|a\| + \|b\| + \|c\| + \|a+b+c\| \geq \|a+b\| + \|b+c\| + \|c +a\|$ in the plane. Gentle hints only, please! I know that attempting to decompose R.H.S. into $$\alpha a + \beta b + ...
0
votes
2answers
174 views

Equations of triangle sides through medians

This has been bothering me for a while. Given a vertex $A(2;-4)$ and the line equations of two medians ($2x-3y-2=0$ and $5x+3y-12=0$), find the line equations on which the triangle sides are. I've ...
0
votes
0answers
105 views

Find a common point that three lines meet.

I have a base 2D triangle with 3 lines coming out of each vertex with their own coordinate point (xyz) and a set distance, is it possible to calculate the specific point that they should meet? I also ...
-1
votes
2answers
83 views

Two objects travel on a 2 dimensional grid. How can i find the angle that must be taken in order for the interception time to be the smallest [closed]

An object (a) travels on a linear path at constant speed. A second object (b) must intercept object a in the shortest amount of time possible. Object b is also at a set speed and can travel in any ...
2
votes
3answers
974 views

Proof of Cauchy–Schwarz inequality

I was reading about the Cauchy–Schwarz inequality from Courant, Hilbert - Methods Of Mathematical Physics Vol 1 and I can not understand what they mean when they said the line that has been ...
2
votes
1answer
1k views

How to calculate the rotation matrix between 2 3D triangles?

I need to calculate the rotation matrix and the translation vector between 2 given triangles in Euclidean space. This is really just a rotation and a translation, the lengths of sides of the triangle ...
1
vote
1answer
207 views

Scalar product equals weighted sum of projection of the vectors onto the edges of a simplex

Given a triangle with the edges $e_1$, $e_2$, $e_3$, it seems (from numerical evidence) that there are coefficients $\alpha_i$ such that $$ u^Hv = \sum_{i=1}^3 \alpha_i \, (u^He_i)\, (e_i^H v) $$ ...
3
votes
3answers
445 views

Heronian triangle Generator

I'm trouble shooting my code I wrote to generate all Heronian Triangles (triangle with integer sides and integer area). I'm using the following algorithm $$a=n(m^{2}+k^{2})$$ $$b=m(n^{2}+k^{2})$$ ...