I'm given the following two lines:  $L_1$: $P_1=(−13, 3, 14)$ with direction vector $d_1=(2, −1, −2)$  $L_2$: $P_2=(5, 4, 4)$ with direction vector $d_2=(−2, 1, 0)$  I'm then asked to find the shortest distance $d$ between these two lines, and then find a point, $Q_1$, on $L_1$, and a point, $Q_2$, on $L_2$ so that $d(Q_1,Q_2) = d$.  So far, I've determined that the shortest distance between these two points can be solved with a projection of the vector $\vec{P_1P_2}$ onto the direction vector found by the cross product of $d_1$ and $d_2$. In this case, it is $(4,8,0)$, or a magnitude of $4\sqrt{5}$.   I'm not really sure how to determine the two points now that I've gotten the distance, any tips or explanations would be appreciated.
Let L1 be the line passing through the point $P_1=(−11, 10, −1)$ with direction vector $\vec d_1=\begin{bmatrix}−2\\ 3\\ −1\end{bmatrix}t$, and let $L_2$ be the line passing through the point $P_2=(−8, 9, 10)$ with direction vector $\vec d_2=\begin{bmatrix}−1\\ 3\\1\end{bmatrix}t$. Find the shortest distance, $d$, between these two lines, and find a point $Q_1$ on $L_1$ and a point $Q_2$ on $L_2$ so that $d(Q_1,Q_2) = d$.   I dont really understand how to properly approach this question, how do i start?
Explanation behind Second Derivative of a Parametric Equation Formula Equation System with 3 variables "Find all the possible solutions $(x,y,z) \in$  $\Bbb R$ that satisfies the following equation system".  My teacher gave me this problem and i got some clues in how to solve it. I evaluated $1$ and $-1$ and i got these solutions $(1,-1,1)$ and $(-1,-1,-1)$. I think these are the only ones but i can't prove it.  Am i wrong?, are there more solutions?.   Thanks  $$ \left\{  \begin{array}{c} x+y-z=-1 \\  x^2-y^2+z^2=1\\  -x^3+y^3+z^3=-1 \end{array} \right.  $$ Ubuntu 16.04 hangs on splash screen during boot Prove that if $\lim_{n \to \infty}z_{n}=A$ then:  $$\lim_{n \to \infty}\frac{z_{1}+z_{2}+\cdots + z_{n}}{n}=A$$ I was thinking spliting it in: $$(z_{1}+z_{2}+\cdots+z_{N-1})+(z_{N}+z_{N+1}+\cdots+z_{n})$$ where $N$ is value of $n$ for which $|A-z_{n}|&lt;\epsilon$ then taking the limit of this sum devided by $n$ , and noting that the second sum is as close as you wish to $nA$ while the first is as close as you wish to $0$. Not sure if this helps.... Word to describe using sarcasm or a similar approach to lead someone to recognise their own mistake How to pass multiple operator properties via UI layout? Basically, I want to have a single operator which can do multiple things, based on some attributes values.  class MyPanel(bpy.types.Panel):     # (...)     layout = self.layout     row = layout.row()     row.operator("my.button", text="Button text")  class MY_BUTTON_OT_Button(bpy.types.Operator):     bl_idname = "my.button"     bl_description = "Button description"     bl_label = "Button"     foo = bpy.props.IntProperty()     bar = bpy.props.BoolProperty()      if bar:         # Do something with foo     else:         # Do something else :P   I know how to set one attribute, like so:      row.operator("my.button", text="Button text").foo=5   But what about multiple arguments? I tried several things that didn't worked, like (e.g.):   With setattr(): row.operator("my.button", text="Button text").setattr(foo=5,bar=True)   With a custom method setVal() in the operator class: row.operator("my.button", text="Button text").setVal(foo=5,bar=True)   Maybe I must use a single EnumProperty? I hope to avoid this, so my question is: Is it possible to pass multiple custom arguments to set attributes in an operator class? And if yes, how ?  Thanks for your help. Smooth reload of uitableview data when rows are deleted Show that a matrix is nilpotent. Let $A,B \in \mathbb{M}_n (\mathbb{C})$. If $A^2B + BA^2 = 2ABA$ then exist $k \in \mathbb{N}$ where $(AB-BA)^k = 0$.  I tried solve with minimal polynomial, but I did not have much effect. undelete big files - mission impossible? I've accidentaly deleted outlook.pst (6.7GB) file, while there was only 400MB free space left on primary NTFS partition (winxp).  I've tried several recovery tools to get this file back. "Ontrack Easy Recovery Pro" found 0 pst files (complete scan mode), while "Recover My Files" in sector scan mode found 5 pst's, but 4 of them of sizes from 3 to 28 KB, while the 5th one - 1Gb.  I've managed to succesfuly recover 1Gb pst file, which was 1 year old copy (the one used after the latest windows reinstall).  Now, I'm frustrated and confused   Why 1 year old file was succesfuly recovered if there were only 400MB left on primary partition? Where's 6.7GB file gone? I did some reading (), and it seems that there's almost no probability to retrieve the file I'm looking for, but wait - none of recovery tools i've used found zero-sized pst file, moreover - if due to fragmentation a file might be corrupted - we could use scanpst.exe to fix some errors and survive with 10 or 100 emails missing - whatever. Could you please recommend some more sophisticated recovery tools for this particular task?   Appretiate your help - thanks in advance SVM for unbalanced data I want to attempt to use Support Vector Machines (SVMs) on my dataset. Before I attempt the problem though, I was warned that SVMs dont perform well on extremely unbalanced data. In my case, I can have as much as 95-98% 0's and 2-5% 1's.   I tried to find resources which talked about using SVMs on sparse/unbalanced data, but all I could find was 'sparseSVMs' (which use a small amount of support vectors).  I was hoping someone could briefly explain:   How well SVM would be expected to do with such a dataset   Which, if any, modifications must be done to the SVM algorithm What resources/papers discuss this If someone could help me with the proposed change of variables, it would be greatly appreciated. Consider Euler's equation:  $$z^2w'' + \alpha zw' + \beta w = 0$$  where $w$ is a function of $z$ and $\alpha, \beta$ are constants. How would the change of variables $t =\ln(z)$ transform this equation? Why is that when I open up my file in blender, the reference picture is gone When you are using a reference picture in blender, do you have to keep it? Do the pictures have to stay in your computer? I sometimes delete my reference images, because I'm on my mother's computer and any file I download has to go away. When opening my blender file the pictures are gone. How can I get my reference images to stay in my blender file even if the original file is deleted? Well, luckily I got this error on my test environment. I'm so scared about this error that I disabled all logon triggers I was using on production environment.   I created the famous logon trigger, and I put a database in offline mode just to mess with something else. Then I discover that because the trigger can't find the table, I can't access the instance anymore. There are plenty of questions related to this, but even doing everything I could find, I still can't acces the instance, not even with SQLCMD.  I'm doing this:  sqlcmd -S server\instance -U sa -P &lt;pass&gt;  -A   If I don't use -A I receive the famous error:  logon failed for sa due trigger execution.   If I use -A:     Sqlcmd: Error: Microsoft ODBC Driver 11 for SQL Server : SQL Server   Network Interfaces: An error occurred while obtaining the dedicated   administrator connection (DAC) port. Make sure that SQL Browser is   running, or check the error log for the port number [xFFFFFFFF]. .   Sqlcmd: Error: Microsoft ODBC Driver 11 for SQL Server : Login timeout   expired. Sqlcmd: Error: Microsoft ODBC Driver 11 for SQL Server : A   network-related or instance-specific error has occurred while   establishing a connection to SQL Server. Server is not found or not   accessible. Check if instance name is correct and if SQL Server is   configured to allow remote connections. For more information see SQL   Server Books Online..   Why i'm not able to connect to the sql server    sql server express here.  I could enable SQL Browser, but I still can't access it.  I don't think this question is duplicated because is not about the trigger, is about Why I can't access the server with SQLCMD. I pretty much know how to fix this. I just don't know how can I acces sql server without triggering the trigger. As it is common with people from my country, I have an immense difficulty with prepositions in English, especially with the use of in and on.   When the preposition indicates the position of the object it is a bit easier to decide which one to use, but as it requires thinking from me, I still say things like "I put the bill in the fridge", "my pencil is on my bag", etc, even though if I think about it, I would know how to say it correctly.  Of course, even in those cases where the preposition indicates position the decision is not always clear, as is the case for example with "on the bus" (you are not on top of the bus, you are inside the bus) or "he is in bed" (you are not inside the bed, you are on top of your bed).  Other cases are even less clear, and I believe there is no real rule to decide what should be said; the person should just know it. Two examples are "in a bad mood", "you are on my mind".  So my first question is whether there is really no rule to help me. The second question refers to two of the cases where I still don't know whether to use in or on:   good luck on/in your exam in/on the list   The last one is especially important to me, as I have asked a number of native speakers, and each time I get a different answer. The only consensus seems to be the case where you say "on top of the list". Apart from that, some people will say that I should say "his name is in the list" whereas others think I should say "his name is on the list". And yeah, a couple of people did tell me that I can use either.  Can someone help me? A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity Let $A \in \mathbb{C}(n,n)$ and $k \geq 2$ be an integer such that $$A \sim A^k$$. Show that if $A$ is non-singular then each eigenvalue of $A$ is a root of unity.   Attempt: Since $A \sim A^k$, $$PA = A^kP$$ where $P$ is an invertible matrix. Since $A$ is invertible, $0$ cannot be an eigenvalue of $A$. Suppose $$Av = \lambda v \quad v \neq 0$$ then $$PAv = \lambda Pv$$ $$\therefore A^k(Pv) = \lambda (Pv) $$ but this implies that $Pv$ is an eigenvector of $A$. But the eigenvalues of $A^k$ are $\lambda^k$ $$\therefore \lambda^k=\lambda$$ which gives the conclusion required.   My questions is: Is the logic correct? If so, Am I missing any details? If not, then how could I approach this?   Thanks! Ubuntu files worthless on Windows? Why are two different concepts both called "heap"? Can't delete folder in Windows 7 I'm trying to delete a folder in Windows 7 and get a perplexing error message: "Could not find this item:  This is no longer located in G:\Graphics.  Verify the item's location and try again.  I can see the folder -- I can find it.  I just can't delete it.    I also get a second error message (sometimes) when I click on the folder: G:\Graphics 2009-11-17 refers to a location that is unavailable...this information might have been moved to a different location.    I'm using Windows 7; this folder is on an external hard drive.  I've emptied the folder (there were items in it); I've scanned that external hard drive for errors.  Trying to rename the folder yields the same enigmatic error message.    Is there a way to delete this folder? How to use a proxy on the command line? I can set my proxy username and password along with proxy settings in the proxy ui but these settings do not work on the command line. How can I use apps such as wget &amp; ping on the command line with a proxy?  Example Details:   username: 1234 pass: linux proxy: proxy port: 8080 Is static HTML the fastest? I have been researching several different techniques to deliver web content fast, like nginx and node.js.  When it comes down to performance optimization http expires headers and gzip come to mind. After that come common techniques like sprites and CDNs etc.  But I am wondering.  What would be the very fastest technique to load a website?  Is static html the very fastest that can be? Or is there something else even faster?