Tagged Questions

Use this tag for questions involving vectors, which are elements of vector fields.

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Counting number of points making angle < 90

I have a around 1000 points and 1000 segments in the form of $(x_1, y_1, x_2, y_2)$ meaning the segment starts at coordinate $(x_1, y_1)$ and finishes at $(x_2, y_2)$. For each line i want to know how ...
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Equality of vector & Directions

Is the direction 120° west of the South Axis same as the direction 30° north of the West Axis (both from a fixed observational point).
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Link between geometric vector(which i knew in school) and vector as a matrix?

What's the link between a vector (a one dimensional matrix) and a geometric vector (a line representing magnitude and direction)?I know that matrix is just a rectangular arrey and my second question ...
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A book on Vector Calculus with emphasis on geometrical intuition

I am a physicist trying to learn vector calculus in a way that is a mixture of the way mathematicians learn it with the way that physicist learn it in order to be able to learn Differential Geometry ...
36 views

finding the angle between two vectors

If $a,b$ and $c$ be three vectors such that $|\, a \,|=3$, $|\, b \,|=5$ and $|\, c \,|=7$ and $a+b+c=0$. Then find the angle between $a$ and $b$. I tried by taking $a=-(b+c)$ and $b=-(c+a)$. But ...
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Vector and Scalars

The median PS of a triangle PQR is bisected at L and QL is produced to meet PR at M. Prove that: $$PM=(1/3) PR$$ I tried by taking P as the origin and q and r as position vector of Q and R ...
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Direction of a gradient at maximizer on the boundary

Let $u \in C(\bar{B})$ where $B=B_1(0) \subset \mathbb{R}^n$ is the unit ball. Assume $u$ attains its maximum at $x_0 \in \partial{B}$ and $\nabla u(x_0) \neq 0$. What can we say about the direction ...
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Why shift the result of subtracting vectors?

Why do we shift the resulting vector after subtracting any two vectors a and b? I learned that when you add any two vectors a and b, the sum vector looks like the one that can be seen in the picture ...
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How to find the maximal length of a system?

Let P be the set of $(a,b,c)^t \in \mathbb{R}$ which satisfies the following inequalities: $-2a+b+c \leq 4$ $a-2b + c \leq 1$ $2a + 2b-c \leq 5$ where $a \geq 1$, $b \geq 2$, and $c \geq 3$. ...
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derivative and curl vector notational difference

This must be a really trivial question, and I am not sure I am allowed to post these here. Just wanted to know but didn't know what to search. What is the difference between $\overrightarrow {dr}$ and ...
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What are linearly dependent vectors like? [closed]

How are they different from linearly independent vectors?
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Monotonic vector linear trasformed to another monotonic vector

Let $b = (b_1,\ldots,b_n)\in \mathbb{R}^n$ such that $\forall i \in \left\{ 1,\ldots, n \right\}$ we have $b_i > 0$ and $\forall i \in \left\{1,\ldots,n-1 \right\}$ we have $b_i > b_{i+1}$. Let ...
Consider the ellipse $r'(t) = \langle3\cos(t),4\sin(t)\rangle$ for $0\le t \le 2.$ (a) At what points $\|r'\|$ have maximum and minimum values? (b) At what points does the curvature have ...
I learned that we can get the component of a vector in any direction using the dot product. The problem I have is the meaning of the term component itself. The component of a vector $\vec A$ in the ...