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

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12 views

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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0answers
8 views

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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3answers
31 views

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 ...
2
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1answer
31 views

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 ...
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1answer
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 ...
0
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1answer
20 views

The relation of correlation coefficient of the sum of two vectors.

Does the correlation coefficient of the sum of two vectors between the correlation coefficient of each of them. Suppose I have three vectors $x_1,x_2,x_3$. The correlation coefficient of $x_1$ and $...
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1answer
27 views

Notation for set of unit vectors

Is there a standard notation for the set of unit vectors $\{\vec v\ :\ |\vec v|=1\}$?
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2answers
25 views

Solution of a simple vector equation

Consider the following equation $\lambda (a+Pu)=\lambda^* (a+Pu^*)$, where $\lambda$ and $u$ are the variables, $\lambda,\lambda^* \in \mathbb{R}$, $u, u^* ,a \in \mathbb{R^n}$ and $P \in \mathbb{R^{...
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0answers
18 views

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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0answers
11 views

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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2answers
32 views

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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0answers
16 views

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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0answers
21 views

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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2answers
30 views

Solving vector equation 3

Solve for $\bar{x}$ and $\bar{y}$ $$\bar{x}+\bar{y}=\bar{a},~~ \bar{x}\times \bar{y}=\bar{b},~~ \bar{x}.\bar{a}=1$$ Attempt: $\bar{x}+\bar{y}=\bar{a}$ dot by $\bar{a}$, we get $1+\bar{a}.\bar{y}=|...
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1answer
29 views

Solving vector equation 2

Using vector method, show that the vector equation $$\bar{x}\times \bar{a}+(\bar{x}.\bar{b})\bar{c}=\bar{d}$$ is satisfied if $$\bar{x}=\lambda \bar{a}+\bar{a}\times \frac{\bar{a}\times (\bar{d}\...
2
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0answers
39 views

Why is this Isometry an rotation?

i need a little help. Did someone have an idea how to prove this? Thanks in advance. Be $\Phi$ an direct isometry of the euclidean Space $\mathbb{R}^3$ with $\Phi (\left(\begin{eqnarray} 2\\0 \\1 \...
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1answer
53 views

Solving vector equation 1 [on hold]

Using vector method solve $p \bar{x}+\bar{x}(\bar{x}.\bar{b})=\bar{a}\times \bar{b}+\bar{c}$ How to solve $\bar{x}$ from such vector equation. Please help.
2
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1answer
48 views

Dual basis vectors and Basis one-forms

I'm studying Tensor Calculus on some MIT's notes (page 16) and I'm stuck at the point where it defines dual basis vectors. I have already studied basis one forms and I can't understand why we need to ...
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0answers
15 views

Vector elements converging to the same value - a proof by contradiction

Note: I'm going to simplify the proposition and proof in this question a bit to avoid a large number of definitions and theorems - hopefully I don't remove anything vital. I'm afraid the material here ...
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0answers
34 views

How calculate intersection directly without Stokes' theorem?

Calculate the line integral directly without Stokes' theorem: \begin{gather*} \oint_\gamma \mathbf{F} \cdot d\mathbf{r} \end{gather*} \begin{gather*} \mathbf{F}(x,y,z)=(2z-3y) {\hat{\mathbf{i}}} + (3x-...
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0answers
22 views

Vectors applied on the arm [closed]

I just received a maths question saying the body and its joints are subject to significant forces under load. Your challenge is to redesign a part of the body, and using vectors, explain how it could ...
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1answer
17 views

How do I prove that the layered vector product A × [B × (C × D)] = B[A · (C × D)] − (A · B)(C × D)?

Given the layered quadruple vector product A × [B × (C × D)] and by using simple vector identities prove it is equal to B[A · (C × D)] − (A · B)(C × D). I attempted to use the vector triple product ...
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0answers
10 views

Two vectors are equal with given magnitude of resultant vector. find magnitude of both vectors [closed]

Two vectors are equal such that $a$ is equal to $b$ and the resultant vector of these vectors is equal to $1263$. Find magnitude of vectors?
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2answers
30 views

A basic question on the Del symbol / gradient

I have a very basic question regarding the $\nabla$ (Del) symbol / gradient on a field (which I have called f). I have seen two definitions of this symbol: $\nabla f = (\frac{\partial f}{\partial x},...
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2answers
25 views

How to normalize and inverse a vector so it sums to 1 ?

I understand how normalization works. You sum up the individual values of the vector, you divide each value by the sum, and voila... they sum to 1. Why doesn't it work when you subtract them from ...
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2answers
38 views

Sub Vector space

Is the following set Sub vector space of $R^2$ ? $$K=\{(x y) \in R: x^2+y^2=1\}$$ Well, it was easy to prove that the set is not empty. But Problem is if i take $u,w \in K$. How to prove also $u+w ...
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1answer
24 views

Question about vectors, planes and lines

Let $O,A$ be two points in the plane with $|\vec{OA}|=3$. Which line is formed by the points $M$ of the plane, such that $\vec{OM}(\vec{OM}-2\vec{OA})=7$ ? My attempt.. Suppose $\vec{OM}=\vec{x}$ ...
2
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1answer
29 views

Vector as a linear combination of other Vectors

I have a set of vectors and in $\mathbb R^3$ in a $3\times 6$ matrix already in row-reduced echelon form. I had to express one of $v_1(1, 0, 0), v_3(0,1,0)$, and $v_6(3,-2, 0)$ as a linear combination ...
2
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0answers
53 views

Rotation Matrix which maps a point to an specific point

How can I compute the rotation matrix which rotates an $n$-dimensional vector $\vec{A}$ around an $n-D$ vector $\vec{O}$, and maps it to a vector $\vec{B}$ (while $\vec{A}, \vec{B}, \vec{O}$ are known)...
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1answer
26 views

Efficient assignment of tetrahedron's chirality

Suppose we have a regular tetrahedron delimited by four points $A_{1}, A_{2}, A_{3}, A_{4}$. There are 24 permutations of vertices, but there are only two distinct terahedra that cannot be ...
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1answer
28 views

How can I calculate the angle of a line/vector if the center of the image is not (0,0)?

Simple image about the problem How can I calculate the alpha? My center of the image is (320,240) because it is a 640x480 image and the upper left corner is the (0,0). I tried to calculate it with ...
2
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1answer
65 views

Is the angle between a and b is equal to the angle between b and a?

This was a question in an exam: Calcualte tan of the angle between a and b if:a = (4,3) and b = (5, -12) There are two answers to this question: Some students devided the dot product of a and b by ...
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3answers
47 views

Determine if the following vectors are coplanar.

I have no idea to start with this question, I know how to find if vectors are coplanar when the values of the vectors are given to me, but I do not know how to manipulate coplanarity properties well ...
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0answers
43 views

Can vectors have negative magnitude?

As part of my master's thesis in computer science, I am writing about a system which uses the following formula: $$ c = \|\vec{a}\| \times \left| \sin{\left(\angle{\vec{a}} - \angle{\vec{b}} \right)} ...
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1answer
27 views

Comparison of Cartesian and Scalar Notation in Mechanics

In his book on Engineering Mechanics - Statics, R C Hibbeler provides many force problem solutions in both scalar and Cartesian notation (e.g Example 2.5 Chapter 2). It feels like he is trying to ...
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1answer
23 views

Associative law of scalar multiplication of a vector

If a,b are two real numbers and v is a vector, prove that: a*(bv) = (ab)*v. I am trying to prove this equality by not using the fact that a vector can be represented by coordinates, but just by ...
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2answers
32 views

Write the vectors u, v, w, z in terms of a and b.

Write the vectors $u, v, w, z$ in terms of $a$ and $b$. I'm unsure of how to do this.. If someone could give me an example of one being done I'm almost positive I could mimic it and figure out the ...
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1answer
25 views

Collinear Points in 3-Dimensions

The points A(3, -1, z), B(1, 2, 6), and C(x, 8, 14) are collinear. Find the values of x and z. I have tried finding common ratios between the points, but no common ratio is possible, I have a feeling ...
2
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1answer
51 views

Is it possible to add vectors that don't have the same initial point or terminal point?

I have read in couple of books that describe addition of vectors not acting at the same point. They describe it by saying we have to bring the initial point of one vector to the other and then resolve ...
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2answers
28 views

Finding possible values in vector.

Just having some difficulty finding the values of '$P$' in this vector. Relative to an origin $O$, the position vectors of the points $A$ and $B$ are given as follows: $\left\lvert OA \right\rvert$ =...
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1answer
15 views

3-Space Vertices of a Parallelogram

The points (1, -2, 4), (3, 5, 7) and (4, 6, 8) are three of four vertices of parallelogram ABCD. Explain why there are three possibilities for the location of the fourth vertex, and find the three ...
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1answer
29 views

How to rotate a 3D vector on the surface of a plane by a known angle?

Available data The plane β which is defined by a normal vector n and point P. The vector v which lies on the surface of the plane.(the angle between v and n is 90 degrees). The angle α to which v ...
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2answers
30 views

Find the nearest point

How can I find the nearest point of the set(M) to the point (A) in GENERAL(with different set or in 3D space )?
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18 views

Is it better to average the log2 for a series of numbers or just the numbers themselves? And, how would you test or prove this?

Lets say I'm trying to compare two vectors for similarity and normalizing them before hand based on some mean or standard deviation combo for the purpose of finding the similarity between the 2 ...
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1answer
35 views

Given the parallel and perpendicular component of a vector in terms of another vector, how do you determine the tensor that connects both?

Sorry for the awkwardly phrased title, I wasn't sure how to properly word it. I want to do the following: I have a vector $\vec J$ and a vector $\vec E$ with the following relation (with the ...
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3answers
38 views

Angle between A vector and B vector from given data: $\ |A-B|=\sqrt{3}\ |A|$ [closed]

The two vectors $\vec A$ and $\vec B$ are of equal magnitude and such that $|\vec{A}-\vec{B}|=\sqrt{3}\ |\vec A|$. The angle between $\vec A$ and $\vec B$ is: (A) $60°\ \ $ (B) $90°\ \ $ (c) $120°\ \ ...
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2answers
61 views

What are linearly dependent vectors like? [closed]

How are they different from linearly independent vectors?
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0answers
22 views

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 ...
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1answer
12 views

Finding maximum and minimum values of the rate of change of parametric graph

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 ...
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1answer
21 views

Understanding components of a vector

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 ...