# Tagged Questions

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### Finding the vertices of a square - straight lines

Question: Each side of a square is of length $6$ units and the center of the square is $(-1, 2)$. One of its diagonals is parallel to $x + y = 0$. Find the co-ordinates of the vertices of the square. ...
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### How to find an equation of a plane perpendicular to two other planes and passing through a point

Please, could anybody help me with the next problem. I have two planes: $$2x-y+5z+3=0 \ (\text{red plane})\\ x+3y-z-7=0 \ (\text{green plane})$$ And I need to find a plane which is perpendicular ...
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### Getting coordinate vector in linear algebra

I know how to get the coordinate vector of single matrices by just joining them and doing a gauss jordan. But these are a 2x2, I don't know how to go about this, apparently no elimination can take ...
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### how to calculate the coordinates center of a squar [closed]

I need to calculate the center of square cells each cell has 4 (x,y) coordinates. Can one help me to Know how can I calculate the coordinates of the center of each cell?
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### What is a coordinate system?

What's a coordinate system? I was watching a Khan video about coordinates with respect to orthonormal bases. It is mentioned that orthonormal bases make for "good coordinate systems". I didn't ...
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### What does the phrase “uncoupled across coordinate directions” mean in this text?

The following paragraph is from a paper about comparison of maneuvering target tracking models.In the paragraph it talks about constant acceleration models. The above models are simple but crude. ...
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### Change of Basis - Homework Question

Please help me understand what is being asked, I feel I am missing something. Compute the change of basis matrix for each of the bases, and use it to find the coordinate vector v with respect to B ...
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### How to find the equation of a line which intersects these lines at 90 degrees?

How to find the equation of a line which intersects these lines at 90 degrees? $p\equiv \dfrac{x}{2}=\dfrac{y+1}{0}=\dfrac{z-2}{1}$ $q\equiv \dfrac{x-1}{1}=\dfrac{y-2}{1}=\dfrac{z+5}{0}$ Since the ...
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### Transfer Transformation from Physics to Vector Graphic

Upfront, I am not a professional in Maths and hope that the formulation of my question describes the problem well enough. I am creating a jump'n'run game, which uses a physics engine (Box2D) and SVG ...
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### How to get coordinates of some area

I have a rectangle and I divide it into 8 triangle with same size. Top left corner is origin. I want to check that if a point is inside the black area or not. Lets say point's x coordinate is pointX ...
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### What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...
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### Origin in vector space?

In the wikipedia article about vector space I do not understand this sentence Roughly, affine spaces are vector spaces whose origin is not specified. A vector space does not need an origin. When ...
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### Rigorous definition and relations between point/vector/affine space/vector space/basis/frame/coordinate system

I am trying to understand the exact relation between all these things: point vector affine space vector space basis frame coordinate system Can you explain me rigorously (in the mathematical ...
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### Great circle and how to “imagine” it in this case?

I am currently working on a riddle. I have to search and locate a person, but I do not know, where he is. I only have some informations, concerning the probability where he might be. A satellite ...
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### Linear Algebra Coordinate Systems

Hi I have a few questions for you guys. I know that every change of coordinate matrix is invertible is true. Is the converse of this statement also true? Every invertible matrix is a ...
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### Coordinate Transformations

I am physics student. My mathematical background is quite weak. I just want to know the similarities (if there are any) between coordinate transformation of two kinds : Rotation of coordinate (and ...
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### Converting from spherical coordinates to cartesian around arbitrary vector $N$

So if I'm given an arbitrary unit vector $N$ and another vector $V$ defined in spherical coordinates $\theta$ (polar angle between $N$ and $V$) and $\phi$ (azimuthal angle) and $r = 1$. How do I ...
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### Coordinate System Rotation and Cross Term

If I have a conic equation $$5x^2 - 4xy + 8y^2 = 36$$ and $\left[\begin{array}{cc} 5 & -2\\ -2 & 8 \end{array}\right]$ in matrix form, whose eigenvalues are 4 and 9, how would I rotate ...
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