# Tagged Questions

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### Difference between Euclidean space and vector space?

I often hear them used interchangeably ... they are very complicated to make any use of. Wikipedia words: Euclidean space: One way to think of the Euclidean plane is as a set of points ...
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### Proving a strange vector inequality in the euclidean space

It seems to hold the following inequality in an euclidean reference frame $(x,y,z)$: $$\overrightarrow{U}\cdot\overrightarrow{U}\ge\sqrt{2}\left(\Omega_x+\Omega_y\right)$$ where: ...
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### How to prove U•V = |U|•|V|cos(θ), if θ is the angle between |U| and |V|

This is a snippet from my book. How did they get from |U|$^2$ = U • V = |U|•|V| |U|/|V| ?
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### Show that a square with vertices t, u, v, w has center 1/4 (t+u+v+w).

I need a help with this question! Show that a square with vertices t, u, v, w has center 1/4 (t+u+v+w).
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### Find vector resultant in rhombus

Uhm I can't find a solution for this problem, perhaps someone can help me with a hint or a solution, thanks in advance :) $$DG=GH=HI=IG\\and\\ AE=EF=FB$$ Find resultant for U+V+W
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### Is there a Taylor series for vector cross product?

I have this equation, where $u,v,w,a,b,Ɵ$ are constants. The RHS comes from the Geometric definition of the LHS $(u,v,w)(a,b,c)=||(u,v,w)||||(a,b,c)||\cos(\theta)$ Expanding the 2-norms ...
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### projection onto vector spaces

How do you project a vector on to the euclidean ball? For example, if there is a vector $x ∈ R^n$ how does one project this onto the euclidean ball. What are the steps for projecting a vector onto a ...
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### What direction does a vector with more than two entries point at?

Say you are given theses two vectors: u = (1, -2, 4) v = (-2, 4, 8) Since there are three entries, how do you know if they point in the opposite/same/different direction?
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### Line-preserving transformations

Is there a name for the class of transformations on the Euclidean plane (or projective plane) that preserves lines? They are not all affine transformations; consider a perspective projection $p$ in ...
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### Are all metric space as a euclidean space?

I believe that all euclidean space is a metric space? But I need to know about inverse? I mean: are all metric space as a euclidean space? Is there any kind of metric space which is not euclidean ...
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### Equation of a line passing through a given point, perpendicular with a vector

Find the line that goes through A(1,0,2) and is perpendicular to r = (-2,3,4) + s (1,1,2) I did a bunch of work, but I don't know if any of it is right. I erased most of it, but this is what I came ...
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### Finding intersection of 2 planes without cartesian equations?

The planes $\pi_1$ and $\pi_2$ have vector equations: $$\pi_1: r=\lambda_1(i+j-k)+\mu_1(2i-j+k)$$ $$\pi_2: r=\lambda_2(i+2j+k)+\mu_2(3i+j-k)$$ $i.$ The line $l$ passes through the point with ...
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### How to fit an object of constant size based on measurements to known points

I'm looking for a mathematical solution for solving where the base of a camera crane (ie a constant square or rectangle of known dimensions) is with measurements to known points. This seems to be a ...
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### Questions related to vectors and linear algebra

1) Given vectors $u = (1, 1, -2)$ and $v = (0, 1, 1)$, find the value of $t$ such that magnitude of $u + t(v)$ has the smallest value I have no idea how to begin. 2) Given vectors $u = (1, 1, -2)$, ...
### Prove that $\vec{EA}+\vec{EB}+\vec{EC}+\vec{ED}=2\vec{EO}$
Let there be a circle $(O,R)$ and $AB,CD$ two perpendicular chords of that circle that intersect on point $E$. Prove that $\vec{EA}+\vec{EB}+\vec{EC}+\vec{ED}=2\vec{EO}$