# Tagged Questions

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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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### How to calculate the points of the triangles making up an Octahedron?

Ok guys, I'm not a great mathematician but will try to work this as accurately as I can. I hope someone can help me. I am drawing some 3D objects and I am having trouble drawing an Octahedron. I ...
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### Unit Vector Based on Angle with XY-YZ-XZ Planes

this may be a simple one but lets assume I have 3 angles (a,b,c) and I want to know what unit vector makes such angles with the XY-YZ-XZ planes. Another question is that I wanna know if a,b and c are ...
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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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### Geometric accuracy analysis of 2d rectangular models

I have reconstructed set of rectangular objects lie on a 2D plane (for ex. ABCD). All these objects are in a one coordinate system. On the other hand, I have reference models for all of them ...
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### Simple way to parameterize two perpendicular vectors

Given are two vectors in $\mathbb{R}^3$, $\bar{u}$ and $\bar{v}$, such that they are perpendicular ($\bar{u}\cdot\bar{v}=0$) and of equal length ($|\bar{u}|=|\bar{v}|$). Is there a "nice" way to ...
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### Can you transform any coordinate from any “space” to another “space” that's defined?

This question pertains to Matrix Transformations. So to provide an example, if I have 3D coordinates where $X = -1$ to $1$, $y = -1$ to $1$, $z = -1$ to $1$. They are "normalized" in my mind. Can I ...
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### Calculate Camera Pitch & Yaw To Face Point

How do you calculate pitch & yaw for a camera so that it faces a certain 3D point? Variables Camera X, Y, Z Point X, Y, Z Current Half Solution Currently I know how to calculate the pitch, ...
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### A vector should more be thought an identity of an entity in space rathar than magnitude + direction?

Can I say that vector is more like a "unique identity" of an entity in space rather than calling it an entity with magnitude and direction ? For example a line. A vector $(10,10,0)$ is the identity ...
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### Can't figure out this transformation matrix

So basically I want to write a transformation matrix to take me out of one coordinate system and into another. The transformation has to be as follows: 1) The positive z axis normalized as ...
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### Vector direction

I have a vector in the 2nd Coordinate of the Cartesian plane. I want to know that how can I find out the direction of the vector that whether it is towards the ...
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### Difficulty understanding the definition of the Barycentric coordinate system

Specifically, the definition at http://en.wikipedia.org/wiki/Barycentric_coordinates_%28mathematics%29#Definition Let $x_1, \dots , x_n$ be the vertices of a simplex in a vector space $A$. If, for ...
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### Test of handedness

I'm reading a book on linear algebra, where the author gives a method to test the handedness or chirality of a given set of 3 basis vectors. if (v1 x v2) . v3 > 0 then it's right-handed, while if ...
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### Finding a coordinate vector for specific basis

I am having trouble with a specific problem concerning coordinate vectors. I have a basis $B' = \{t^2 + 2, t + 3, t^2 + t + 1\}$and a polynomial $p(t) = 4t^2 - t$. so I believed the way to go about ...
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### Triangle and parametric coordinates

I'm studying on a book where it says: "A triangle is the set of points where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
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### Find base from unit vector code - why changing sign?

I have the following code which accepts a v1 vector and outputs two other vectors to construct an orthonormal base ...
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### Doubt on subspace of a vector space

I am new to linear algebra and I have a doubt that : in 2D coordinate system is a line which is at 45 degree NOT passing through the origin a subspace of the vector space comprising the whole 2D plane ...
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### Finding coordinate vector

The coordinate vector of: $$\begin{pmatrix} 1&2&-1\\0 & 0 & 6 \end{pmatrix}$$ with respect to the standard basis of $M2x3$ would be: Are you just finding the inverse of this ...
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### How to move vector(points) coordinates, for a certain angle

I tried several things, but none worked as it should. How to move vector(points) coordinates, for a certain angle that I calculated! I calculated $\beta = 88.7^\circ$. I'd like to expand/skew vectors ...
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### Finding the unit vector indicating direction from A to B

Given vector A and vector B, how can I find the unit vector indicating the direction from A to B? For example (U is the found unit vector): A = 2,3 B = 2,6 U = 0,1 Assume 2D space and low ...
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### Proof of test of collinearity and coplanarity

Statement : If there are 3 points with position vectors a, b and c. Then the points are collinear if and only if there exist scalars x,y,z, not all zero,such that x a + y b +z c = 0 where x+y+z =0. ...
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### Cartesian vector to Cylindrical components

I recently started EE 1, and was confused by the jump from cylindrical coordinates to cylindrical vectors In the past, I've just converted between cartesian and cylindrical via: p = sqrt(X^2 + Y^2) ...
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### Are there derivations of equations of non-degenerate real quadric surfaces

Take the ellipsoid for example $$(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1$$ in the x-y plane you have an ellipse described by $$(x^2/a^2)+(y^2/b^2)=1$$ (suppose z=constant) in the y-z plane you have an ellipse ...
How do I find orthogonal projection of a vector $\vec V_1=(2,3,4)^T$ formed with the points $A(0,0,5)$ and $B(2,3,9)$ on $xy$ plane?