# 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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### What is the difference between a point and a vector?

I understand that a vector has direction and magnitude whereas a point doesn't. However, in the course notes that I am using, it is stated that a point is the same as a vector. Also, can you do ...
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### Row vector vs. Column vector

I'm a student in an elementary linear algebra course. Without bashing on my professor, I must say that s/he is very poor at answering questions, often not addressing the question itself. Throughout ...
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### Cross product in higher dimensions

Suppose we have a vector $(a,b)$ in $2$-space. Then the vector $(-b,a)$ is orthogonal to the one we started with. Furthermore, the function $$(a,b) \mapsto (-b,a)$$ is linear. Suppose instead we have ...
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### Difference between sum and direct sum

What is the difference between sum of two vectors and direct sum of two vector subspaces? My textbook is confusing about it. Any help would be appreciated.
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### What does the symbol nabla indicate?

First up, this question differs from the other ones on this site as I would like to know the isolated meaning of nabla if that makes sense. Meanwhile, other questions might ask what it means in ...
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### What is vector division?

My question is: We have addition, subtraction and muliplication of vectors. Why cannot we define vector division? What is division of vectors?
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### What equation produces this curve?

I'm working on an engineering project, and I'd like to be able to input an equation into my CAD software, rather than drawing a spline. The spline is pretty simple - a gentle curve which begins and ...
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### how does the dot product determine similarity?

I want to know how the dot product can determine whether two vectors are similar? I know that the formula $$\cos(\theta) = \frac{u \cdot v }{ ||u||\,||v||}$$ means something, but don't know what.
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### Why is the SVM margin equal to $\frac{2}{\|\mathbf{w}\|}$?

I am reading the Wikipedia article about Support Vector Machine and I don't understand how they compute the distance between two hyperplanes. In the article, By using geometry, we find the ...
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### 3rd type of vector multiplication beside dot/cross product?

I was reading up on how to find the square root of i , and I learned that multiplication of complex numbers could be viewed geometrically by viewing the complex numbers as coordinates on the complex ...
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### In the context of vectors, is there a difference between the terms “magnitude” and “length”?

I noticed vectors are usually said to have "length" and "direction", but then it is said that people want to find the "magnitude". Is this just a difference in terminology or is there something more ...
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### What does this (double absolute value like) notation mean?

Here, $$\left\lVert\frac{\partial\bf x}{\partial s}\times\frac{\partial\bf x}{\partial t}\right\rVert$$ the inside will at last be a vector. and two absolute value signs have covered it. what does ...
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### Euclidean distance and dot product

I've been reading that the Euclidean distance between two points, and the dot product of the two points, are related. Specifically, the Euclidean distance is equal to the square root of the dot ...
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### Standard notation for sum of vector elements?

I can think of multiple ways of writing the sum of a vector $\mathbf{v}$'s elements, but is there a standard operator for this? Using "programming" notation it is typically sum($v$), but this seems ...
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### Formula to project a vector onto a plane

I have a reference plane formed by 3 points in $\mathbb{R}^3$ – $A, B$ and $C$. I have a 4th point, $D$. I would like to project the vector $\vec{BD}$ onto the reference plane as well as project ...
I would like to write mathematically, if possible, the following statement: Given a vector $x=[1,4,5,3]$ and an integer $j=3$, find the position of $j$ in $x$? How to write this mathematically? ...