1
vote
0answers
32 views

System of quadratic equations for a tetrahedron

I know the dimensions of the base of a tetrahedron and the angles between the non base sides at the apex. I want to know the lengths of the three non base sides. Let the base's corner points be $A, ...
0
votes
2answers
54 views

How to find the intersection points of lines that are normal to two curves?

Let I have two curves, \begin{gather} f(x)=\frac{x^3}{4}+1 \\ g(x)=\frac{(x-\tfrac{1}{2})^3}{7}+\tfrac{1}{2} \end{gather} There are zero or more lines that are normal to both curves. In other words, ...
0
votes
2answers
19 views

What is wrong with this technique for proving skew lines?

We have the following set of lines: $$L_1: \frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-1}{-3}$$ $$L_2:\frac{x-3}{1}=\frac{y+4}{3}=\frac{z-2}{-7}$$ This leads to the following parametric equations: ...
0
votes
1answer
17 views

How to Do Trilateration?

Trilateration is the process of calculating the coordinates of a point by using its distances to three other points. Say that, we have three points of which we know the coordinates: $A(A_x, A_y)$ ...
0
votes
0answers
31 views

determine in what grid rhombus is a point

i have a rhombus ( i.e. diamond) grid determined by these equations ...
1
vote
0answers
77 views

Geometry aspect of a extreme value problem

In a plain with orthogonal coordinate $XOY$, set point $A(a,a)$, and $P$ is a point in function $y=\frac{1}{x}$,where $x>0$. If the distance between $P$ and $A$ is $2\sqrt{2}$.Find all $a$ ...
0
votes
0answers
26 views

Find angle-preserving transformation matrix given 2 points

I asked a similar question yesterday about finding an affine transform matrix given the same 2 points in both coordinate systems. I was told that there was only a unique solution, if the scaling was ...
3
votes
2answers
54 views

Solution for line intersection without special cases

Say that we have two lines in two dimensions along the points $\vec{m} + s\vec{k}$ and $\vec{n} + t\vec{j}$ and we want to find the $s$ and $t$ for where these lines intersect. The obvious solution ...