# Questions tagged [vectors]

Use this tag for questions and problems involving vectors, e.g., in an Euclidean plane or space. More abstract questions, might better be tagged vector-spaces, linear-algebra, etc.

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### Want to get knowledge about vector

"Basically, when we multiply 2 by 3, we get 6. Here, 3 times 2 equals 6. Similarly, when we multiply vector A by vector B, we might expect to get AB. However, instead of AB, we get AB times ...
2 votes
0 answers
47 views

### Does the eigenvectors for the sum of projections onto unit vectors that sum to zero imply a symmetry of the set of unit vectors?

I am interested in a sum of projectors $A = \frac{\text{Tr}(A)}{N}\sum_{i=1}^N \mathbf{a}_i\,\mathbf{a}_i^T$, where $N$ is the total number of unit vectors, $\mathbf{a}_i$ is a real column vector with ...
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3 votes
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### Difficulty understanding why dot product is necessary in solving the angle between line and a plane

A line with equation $L = (1, 0, -2) + s(2, -1, 2)$ intersects with the plane $x + 2y + z = 2$ at an angle of $\theta$ degrees. I am having some difficulty understanding why the dot product is ...
-3 votes
0 answers
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### Numerical analysis - matrix [closed]

My matrix: 3 -1 1 = 6 -2 5 3 = -22 3 -3 5 = 20 I couldn't figure out how to solve the exercise and would appreciate an answer Find a pair of vectors ...
2 votes
1 answer
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### Confirming the angle between intersecting planes using projections

Let's say I have 2 planes: $$\text{Plane}_1: x + 2y - z = 3$$ and $$\text{Plane}_2: 2x -y +3z = 4$$ which have normal vectors of $[1,2,-1]$ and $[2,-1,3]$ respectively. It's clear that the normal ...
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6 votes
2 answers
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### Is a scalar presented as a matrix or not here?

In the linear algebra course I am taking, the inner product of 2 vectors $\langle u, v \rangle$ is defined as being a scalar; however, it is also viewed as being a product of 2 matrices as $u^Tv$, as ...
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6 votes
6 answers
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1 vote
1 answer
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1 answer
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### If $F(x)=(F_1(x),\dots, F_n(x))$, is always possible to find $F_i(x)=\min\{F_1(x),\dots, F_n(x)\}$?

Let $n\ge 2$, ($n$ finite) and $F:\mathbb R\to\mathbb R^n$ be a positive function, meaning that $$F(x)=(F_1(x),\dots, F_n(x))$$ and $F_i(x)\ge 0$ for any $i\in\{1,\dots, n\}$. My question is: is ...
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### Interpretation of a vector quantity

Suppose we have a vector field $\vec{A}$ in $\mathbb{R}^n.$ The following “vector quantity”: $$(d\vec{r} \cdot \nabla)\vec{A}$$ looks strange perhaps, but when expanded is seen to be a simple quantity:...
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1 vote
1 answer
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### Angle of attack between surface and vector

I'm trying to make a simplified sailing ship simulation and want to get the angel-of-attack between a surface normal vector (representing a sail) and a vector (representing the wind velocity). The ...
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-1 votes
1 answer
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### Cosine similarity magnitude vector

there is one thing I'm not sure about regarding cosine similarity. Does the magnitude of the vector matter? I think the answer is yes, especially if you look at the picture below where the word count ...
0 votes
1 answer
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### Is there an algorithm for sorting points in a field based on sweeping a line through them at an arbitrary angle?

Given a set of coordinates on a euclidean plane, is it possible to sort the points by sweeping a line through them where the line might not be strictly horizontal or vertical? The inputs to the ...
-1 votes
0 answers
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### If $V={v_{1},v_{2},...,v_{n}}$ is an orthogonal set, determine if $\sum_{i=1}^{n}\left\| v_{i} \right\|=\left\| \sum_{i=1}^{n}v_{i} \right\|$ [closed]

If $V=\{v_{1},v_{2},...,v_{n}\}$ is an orthogonal set, determine if $\sum_{i=1}^{n}\left\| v_{i} \right\|=\left\| \sum_{i=1}^{n}v_{i} \right\|$ is true or not. I don´t even know where to start. ...
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1 vote
1 answer
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### Figuring out if an object is headed in the right direction at a crossing?

For a video game, I am trying to figure out whether the ship is headed to the right direction, that is, forward relative to the race direction as it's a racing game in 3 dimensions. Basically, the ...
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### Meaning of $e_{1}$ in $|(s-e_{1})´v|=||s-e_{1}||\cdot ||v||$

(Sorry for any misspelling or gramatical error, I´m not a native english speaker) I am trying to solve this problem: Vector $u=\begin{bmatrix}a &a &a &b \end{bmatrix}´$ can be written as ...
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-3 votes
1 answer
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### Hexagon Consisting of Complex Numbers [closed]

In the Argand plane, the points Q and A represent the complex numbers 4+6i and 10+2i respectively. If A, B, C, D, E, F are the vertices, taken in clockwise order, of a regular hexagon with centre Q, ...
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1 answer
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### projection of vector not equal length of the projection

I have 2 vectors, a and b, from the origin to a plane. The normal vector to the plane, is n. (a dot n) and (b dot n) is the same, and I learned it is equal to the projection of a onto n (and b onto n)....
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### Symplifying a cost function of an optimization problem

Background I have a zero-mean dataset $D(\theta)$ composed by $m$ vectors $y_{1}(\theta)$, $y_2(\theta)$, $\dots$, $y_{m}(\theta)\in \mathbb{R}^2$. Each observation $y_i(\theta)$ depends on a unknown ...
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2 votes
1 answer
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### How to find the number of possible planes equidistant from $5$ points $3$ of which are collinear.

$\vec a,\vec b,\vec c,\vec d$ are four non zero vectors and points $P(\vec a), \; Q(\vec a+\vec b+\vec c), \; R(\vec a-\vec b-\vec c), \; S(\vec d),\; T(\vec a +\vec d)$ are distinct points such that ...
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