So I have a line that looks like this $\begin{pmatrix}1\\2\\-1\end{pmatrix}$ + t$\begin{pmatrix}1\\5\\1\end{pmatrix}$. And I'm trying to find the minimal distance between that line and the line x1 = x2 = x3. I know the find the distance between two lists would be to subtract the lists and the find the length of that but how would I find the distance for two equations like this?
81253
I know how to find the distance between a point and a line, not between two lines.  Find the shortest distance between the lines $(-1,1,4) + t(1,1,-1)$ and $(5,3,-3) + s(-2,0,1)$  Any help would be appreciated.
34491
I guess that I'm missing here something...  How to prove that, if two matrices are similar, then their minimal polynomials are the same one.   Thanks!
100434
Using QGIS - I have a vector of fault lines.  I have point data in the form of a csv which I have also loaded into QGIS.  I need to know how far each point is from the nearest fault line then enter this distance in a new column in the csv file. Any ideas?
14106
I want to draw a TikZ matrix with its border and I would like to define the distance between most external matrix nodes and matrix border. Something like a matrix inner sep. If I change inner sep in matrix options declaration, all nodes inside the matrix also change its inner separation.      I know how to do it with fit library. I just want to know if its possible without it.
67174
I have calculated the parametric form of my line as: $X = (2,2,0) + t(1,2,2)$ and have been given a point $Q = (1,-1,-1)$, how would I calculate the distance from $Q$ to the line?
59926
I would like to find a point $d$ away on a line from a starting point only given a slope. My fist thought was to use the distance formula ($d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$), but I would have to solve for two variables. How can I solve find the point without graphing or brute forcing?
21786
I need to find $X$ from   $$\begin{pmatrix} 1 &amp; 2\\  -3 &amp;-6  \end{pmatrix} X \begin{pmatrix} 1 &amp;2 \\  -1 &amp;-2  \end{pmatrix}=\begin{pmatrix} 2 &amp;4 \\  -6 &amp; -12 \end{pmatrix}$$  I wrote $X$ as   $$X=\begin{pmatrix} a &amp; b\\  c &amp;d  \end{pmatrix}$$  and I got $a+2c-b-2d=2$ but I do not know what to do next. Please help.
82460
How to find the coordinates of the points A and B? If one gets that, then distance formula can be used to find the length.
52006
How can I Tex this equation?  I try to have exactly the same result but for the moment I only succeeded in having intersecting lines... Thanks!
115636
I am quite new to TeX. I want that each line in the following equation be centered, but I cannot find how to do it.  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} \begin{split} a &amp; = \frac{M_{20}}{M_{00}} - x^{2}_{c}, \;\;\; b = 2(\frac{M_{11}}{M_{00}} - x_{c}y_{c}), \;\;\; c = \frac{M_{02}}{M_{00}} - y^{2}_{c}, \\ &amp;\quad x_{c} = \frac{M_{10}}{M_{00}}, \;\;\; y_{c} = \frac{M_{01}}{M_{00}}, \\ &amp;\quad M_{ij} = \displaystyle\sum\limits_{x} \displaystyle\sum\limits_{y} x^i y^j I(x,y) \end{split} \end{equation} \end{document}   Also, it would be awesome if I could write "and" after the first line ;)  Thanks in advance
95347
Find a vector equation for the line through the point $(a,b,c)$ which is normal to the plane through $P(x_1,y_1,z_1), Q(x_2,y_2,z_2) $and $R(x_3,y_3,z_3)$  What would the process be to answer a question like this?
110481
How can we calculate the distance from a point to a plane in normed spaces ? where we are not inner product, for example:  Calculate the distance in $(C[0,1],||\cdot||)$ endowed with the supremum norm $$||f||=\sup_{t\in[0,1]}|f(t)|$$ from the function $f(t)=t^2$ to the linear hull of the functions $g(t)=t$  and  $h(t)=\sin(t)$  Any hints would be appreciated.
4930
Suppose that $P = (1,1,7)$ and $Q = (8,6,1)$. Inside parenthesis are x-coordinate value, y-coordinate and z-coordinate. The question is to find vector and parametric equation for a line segment.   Now, I used equation that goes like $(1-t)&lt;1,1,7&gt;+t&lt;8,6,1&gt;, where, 0\leq t\leq 1$.   But, the answer says that I am wrong. So, I am wondering what is going on.   Also, why do we write parametric equations? Are they really different from vector functions anyway?   If vector function is $&lt;2t,3t,1&gt;$, according to my knowledge, parametric equations would be $x(t)=2t, y(t)=3t, z(t)=1$ ....
52341
I'm trying to find an efficient algorithm for the following problem:  Given two different sets, both of size $N$. Each element in the two sets has coordinates $(x,y)$. The task is to optimize the pairings between these two sets such that the maximum distance between the paired elements given a pairing, is minimized. I have only found algorithms that deal with the squared sum of all distances between paired elements or the smallest distance between any two points from the two different sets.  For example: Given a list of $N$ pair of points that are associated with locations $(x_0,y_0), (x_1,y_1), (x_2,y_2),\dotsc,( x_{n-1},y_{n-1})$, name them $a_0,a_1,a_2,\dotsc,a_{N-1}$ accordingly. And another list of $N$ pairs of different points (locations) $(x_0,y_0), (x_1,y_1), (x_2,y_2),\dotsc,( x_{n-1},y_{n-1})$, name them $b_0,b_1,b_2,\dotsc,b_{N-1}$ accordingly. How can I pair all elements (each element is a pair of points) from list 1 $(a_0,a_1,a_2\dotsc,a_{N-1})$ to the other elements in list 2 $(b_0,b_1,b_2,\dotsc,b_{N-1})$ so that we chose the shortest distances? eventually, I'd need to print the maximum distance among all minimum distances (that we have found for each of the elements). Any idea how can this be achieved in reasonable run time? or name an algorithm that might help here.
33295
Given a line segment from point $A$ to point $B$, how do you find a point $A_2 $ that is perpendicular to the point $A$ at a distance $d$ from $A$? Points $A, B$ and distance $d$ are given.  I cant seem to figure out the correct way to solve this problem and my linear algebra / geometry are a bit rusty. It seems as though using Orthogonal Projection may work since I have the distance but I cant figure out the location of the point. Any ideas?  Take a look at the following Diagram for clarification.
78966
What is the global minimum of the expression   \begin{align} |x-1| &amp;+ |x-2|+|x-5|+|x-6|+|x-8|+|x-9|+|x- 10| \\&amp;+  |x-11|+|x-12|+|x-17|+|x-24|+|x-31|+ |x-32|? \end{align}   I've solved questions of this sort before but there were only 3 terms. I solved those by expanding all the terms in the modulus and drawing a graph. This question came in a paper which requires the student to solve it within 5 minutes. What's a better method?
59270
I have two lines say P1( 0, -1, 0, -1 ) and P2( -1, 0, 0, -1 ). Since I'm working in 2D, there is no Z component. The x,y,z components are normals and the w component is the distance from origin. I am not given the origin or any points on the line.  What method should I use to programmatically determine the point of intersection for these two lines?