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

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1answer
18 views

Index notation in vector functions

Suppose I have a vector $\vec u$ that depends on a vector $\vec x$ and a scalar t, so each component of $\vec u$ depend on all components of $\vec x$. How can I show this relationship with index ...
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17 views

How to find a basis of weight vectors

I have to following Lie Algebra $L=\{x\in End(\mathbb{C}^6)\colon x^tS+Sx=0\}$, where $S=[\begin{smallmatrix} 0&I_3 \\ I_3&0 \end{smallmatrix}]$, and the subalgebra $H$ given by the diagonal ...
1
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1answer
12 views

How to find the normal line of $z = 4x^2 + y^2 - 78$ at $(2,1,-61)$?

How do I find the normal line of $z = 4x^2 + y^2 - 78$ at $(2,1,-61)$? I have found that the tangent plane is $z-16x-2y=95$ but I don't know how to find the normal line. The answer is: $$\frac{2 ...
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0answers
16 views

Increasing or decreasing theta based on direction of vector

I am a programmer, and I have some holes in my math knowledge that I am working on filling in. Right now I'm working with a simple process involving drawing curves and straight lines. The line that is ...
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0answers
13 views

How do you determine a vector of the form $(x,y,z)$ in 3D? [on hold]

Knowing the angle between two vectors, the length of each vector being the same for both, and the $(x,y,z)$ form of one of the vectors with both vectors starting from the origin, how do you determine ...
0
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1answer
31 views

Parametric Problem

i have a question on parametric.. The question states A vector equation $(x,y) = (2,-1) + t(3,2)$. Write as a parametric equation. Show a table with x,y values. Sketch a picture of vector ...
1
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1answer
31 views

Is there another name for a vector?

I am writing a program uses contains both vectors (direction and magnitude) and vectors (a matrix with one row/column) and my head is spinning. I could replace the latter kind of vector with ...
-1
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1answer
18 views

Find coordinates of point C in a equilateral triangle [on hold]

How to find the coordinates of point C in a equilateral triangle, where $A=(-2,2)$ and $B=(6,2)$. http://i.stack.imgur.com/TXjjG.png Thanks in advance
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1answer
30 views

Vector equation of a line

The line $l$ has an equation $r=\begin{pmatrix} 1\\ 2\\ -1 \end{pmatrix}+\lambda \begin{pmatrix} 2\\ 1\\3 \end{pmatrix}$ and equation of plane $p= r.\begin{pmatrix} 2\\ -1\\ -1 \end{pmatrix}$ i) show ...
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0answers
5 views

Convective operator: Distributive with superposition of vector fields?

I'm unable to find a great deal of information on this. I'm mostly sure that the convective operator over a vector field $A$ acting on a function $f$: $$ (A \cdot \nabla )f$$ is distributive, i.e. ...
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2answers
47 views

Matrix or vector product

This is probably a simple question A factory produce a good (1) that requires 3 labor-hours in the assembly department and 1 labor-hour in the finishing department. Assembly personnel receive 19 per ...
4
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3answers
46 views

Vectors sometimes used in math just as arrays/lists of numbers, sometimes as concept of “change”

As a freshman in a small town college. Ive been getting mixed signals to what vectors (and matrices/tensors) are. Sometimes I get the feeling they are used just as containers/arrays for multiple ...
1
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0answers
28 views

Geometrical interpretation of this identity regarding vectors

I tried figuring out what's the geometrical meaning of this identity in vectors. Proving it isn't a problem, however I'd like to know a more geometry oriented explanation to it. I'd appreciate if ...
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0answers
6 views

Angle of the tangent vector of a parabola in function of the angle of the vector that defines this parabola (Apostol, chapter 14.21, problem 1)

Apostol, chapter 14.21, problem 1 (a review problem) Here is the question: Let r denote the vector from the origin to an arbitrary point on the parabola $y^2 = x$, let $\alpha$ be the angle that ...
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1answer
29 views

Can someone help me solve this word problem on vector and magnitude?

A river is 2000 feet wide and flowing at 6mph from north to south. A guy in a boat starts on the east shore and heads west at a normal paddling speed of 2mph. In what direction (measured clockwise ...
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2answers
24 views

Showing vectors are orthogonal [on hold]

Let $u, v ∈ R^n$ be vectors. Show that $u$ and $v$ are orthogonal if and only if $\Vert u + v\Vert = \Vert u − v \Vert$. Can someone put an answer to this so I can compare it to my answer?
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2answers
24 views

Finding a plane perpendicular to two lines and a point

A plane is perpendicular to both [x,y,z] = [1, -10, 8] + s[1, 2, -1] and [x,y,z] = [2, 5, -5] + t[2, 1, -3], and contains the point P(-1, 4, -2). Determine if the point A(7, 10, 16) is also on this ...
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2answers
24 views

Calculate the plane equation of 2 vectors. [on hold]

Which type should I use in order to calculate the plane equation that is defined by 2 vectors, let's say V1 $\langle{1,2,3}\rangle$ V2 $\langle{4,5,6}\rangle$.
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0answers
17 views

Restriction for identification of a indexing vector in sign function

Define the sign function $\text{sgn}(\cdot)$ as $$\text{sgn}(z) = \begin{cases} 1, & \text{if}\ z \ge 0, \\ 0, & \text{otherwise}. \end{cases}$$ My problem turns to be I need ...
0
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1answer
27 views

Difference of inner product space of two vectors

If in an inner product space $\alpha,\beta$ are two vectors such that $\|\alpha\|= 2,\|\beta\|=3$, and $\|\alpha+\beta\|=5$. Then $\|\alpha-\beta\|$ is equal to ? The options are 1)0 2)1 3)√10 ...
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1answer
21 views

let F be velocity vector field of fluid on $R^3$ defined by F(x,y,z)=-yi+xj.

$\newcommand{\Reals}{\mathbf{R}}\newcommand{\Vec}[1]{\mathbf{#1}}$Let $F$ be velocity vector field of fluid on $\Reals^3$ defined by $F(x,y,z) = -y\Vec{i} + x\Vec{j}$. (A) Show that $F$ is ...
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1answer
14 views

Estimate line in [theta, rho]-space given 2 points

Given 2 points (x1,y1), (x2,y2) I wish to estimate a line defined by [cos(θ) sin(θ) -r], where r is the distance from origin to the line along a vector perpendicular to the line, and the angle theta ...
0
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1answer
35 views

proving that two vectors are perpendicular

Let A, B and C be non-colinear points in a plane. Form the triangle ABC, and from each of A and B, draw the line that is orthogonal to the opposite side. These two lines meet at a point D. Now let E ...
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0answers
29 views

Given u and v are two vectors, find ||u×v||² [on hold]

If u and v are two vectors, then the value of ||u×v||² is equal to ?
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2answers
25 views

vectors: finding acceleration

A particle has velocity $3i-2j$ initially and velocity $5i+4j$ 4 seconds later here I tried to find the magnitude if its acceleration,assumed constant ...
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0answers
15 views

How come the angle for cross and dot equations are not equivalent in these equations?

Finding the angle between two lines Given lines: $$l_1 = [3, 1, -1] + t[2, -2, 3]$$ $$l_2 = [5, -1, 2] + t[1, -3, 5]$$ I tried cross product equation of finding the angle: $\cos^{-1}(\sqrt{426} / ...
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1answer
13 views

Finding K such that a line is perpendicular or parallel to a given plane?

Known information: Plane P = 3x -5y + 2z =1 (R^3) Parametrics: x = 5 + t y = 2 - 2t z = -1 - 6t I've solved for t, t = -2. Point of intersection: (3,6,11) ...
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1answer
19 views

Proving vector norm

Quite unsure about this problem. Prove that for vectors $u, v ∈ R^n$ we have $$\Vert u + v\Vert^2 +\Vert u − v\Vert^2 = 2 \Vert u\Vert^2 + 2 \Vert v \Vert ^2$$ Can you just expand the left hand part ...
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2answers
57 views

Show that $\frac{\|\mathbf{u}\, +\,\mathbf{v}\|\, + \,\|\mathbf{u}\,-\,\mathbf{v}\|}{2} \leq \|\mathbf{u}\| + \|\mathbf{v}\|$

I am certain that we need to use the triangle inequality, that is $\|\mathbf{u} +\mathbf{v}\|\leq \|\mathbf{u}\| + \|\mathbf{v}\| $ However, I cannot find a way to proceed from here. Something ...
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1answer
26 views

What is the name of the 3D matrices?

The name of a variable in the $\mathbb{R}$ is called scalar. Multiple scalars form a vector: $\mathbb{R}^n$ Two or more vectors form together a matrix: $\mathbb{R}^{n \times m }$ But what is the ...
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0answers
34 views

Basis of all real polynomials?

I am studying the book Topics in Algebraic Graph Theory by Beineke et all and the page 12. By the book, the set of all real polynomials can be generated by the set $\{1,x,x^2,\ldots\}$ which I ...
0
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1answer
25 views

Proving Transformation defined as a matrix is linear

I came across a problem thatwhile doing some review that states: Consider the transformation $\textit{T}$:$\mathbb{R}^2\rightarrow\mathbb{R}^2$ defined by the matrix $$ \begin{pmatrix} ...
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0answers
21 views

Did I interpret this wiki article on spherical interpolation correctly?

In Lua pseudocode, I believe the wikipedia article here is saying that the formula is used in the following way: ...
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0answers
10 views

How do I find if a point is intersected by two or more 3D vectors, and if so; where they intersect? [closed]

I have the line equation in the form $\mathbf r = \mathbf p + s\mathbf d$, where $\mathbf r$ = the position vector of any point on the line $\mathbf p$ = the position vector of a particular point on ...
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1answer
29 views

Question is about vectors? [closed]

In each part find the Vector component of V along B and the vector component of V orthogonal to B. 1. V = 2i - j , B = 3i + 4j 2. V = (4 , 5) , B = (1 , -2)
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0answers
10 views

How to normalize feature vectors when concatenating [closed]

I have two different feature vectors of completely different scale, which are to be used as training data for machine learning algorithm. When I concatenate them, should I scale and normalize them ...
-1
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1answer
28 views

Transpose of a vector: Find values to be not perpendicular

I have a question in my work where I have to find the values of a and b such that (a,2,3)^T and (1,2,b-2)^T are not perpendicular. (I have chosen random values as an example, as I'm not asking anyone ...
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0answers
25 views

Does 3D euclidean space allows vector sum in 2 dimensions?

Is this right to add two orthogonal vectors to to get one vector, using this vector in calculations and after getting results, decomposing result vector to get orthogonal components? I am a ...
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0answers
14 views

When we take curl of a vector field is it not affected by any singular point unlike divergence of that field?

In $(r, \theta, \phi )$ coordinate system $\nabla\cdot\frac{\hat{r}}{r^2}=4\pi\delta^3(\vec{r})$ . There is this $\delta^3(\vec{r})$ because $\frac{\hat{r}}{r^2}$ blows up at point $r=0$ But ...
2
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1answer
27 views

Equations of all planes containing a given line, and at a particular distance from origin.

I have the line $G=\{x=(1,2,3)^T+t(1,0,1)^T∈R^3:t∈R\}$ The problem is to determine all planes $∈ R^3$ in the normal form containing $G$ and having distance $\sqrt{2}$ from the origin. What I have ...
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2answers
31 views

Find the orthogonal projection of a vector v onto U

I am trying to solve this question: Let $u$ be a unit vector in $R^n$ and let $U$ be the subspace spanned by $u$. Show that the orthogonal projection of a vector $v$ onto $U$ is given by ...
2
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1answer
20 views

Path from a start point at a certain heading to an end point at a certain heading while obeying a minimum turn radius

So not sure if my title is clear (also no idea what to tag, because you need 1000 rep to add tags) so I will try my best to explain the problem. I'm working in 2D space and to simplify the problem, ...
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1answer
159 views

Orthogonal projection question

Consider the (orthogonal) projection $T: \mathbb{R}^3 \to \mathbb{R}^3$ onto the plane $x - y + z = 0$. (a) Find the standard matrix $[T]_S$ for $T$. (b) Find a new basis $B$ so that ...
1
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1answer
17 views

How to “simplify” parallel vectors in $\mathbb{C^3}$?

Sorry for the bad title but I can't find a better one. $\vec{v}=(v_1,v_2)^T\in\mathbb{R^2}$ $-\vec{v}=(-v_1,-v_2)^T$ For my needs $\vec{v}$ and $-\vec{v}$ are equivalent. In my problem $\vec{v}$ is ...
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3answers
37 views

Angle between $\left(\vec{u} + \vec{v}\right)$ and $\left(\vec{u} - \vec{v}\right)$ [closed]

Given that the vectors $\vec{u}$ and $\vec{v}$ are not null, can we state that the angle between $\left(\vec{u} + \vec{v}\right)$ and $\left(\vec{u} - \vec{v}\right)$ is $\pi/2$? If so, how can one ...
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0answers
10 views

How to find contravarient components in this example?

I am wondering how to ffnd contravarient basis vector in terms of covariant in this example on this Wikipedia page ...
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2answers
37 views

Terminology for constructing a vector or matrix of the coefficients of an expression

I have a vector of variables as follows: $$ X= \begin{bmatrix} x_{1} & x_{2} & \dots & x_{n} \end{bmatrix} $$ I also have a function $f$ which returns a linear combination of the ...
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1answer
30 views

Angle between planes challenging Question

The plane $r.(a,3,5)=10$ is inclined at an angle of $45^\circ$ to the plane $r.(-5,1,4)$ Find the value(s) of $a$ up to $2$ decimal places. I attempted this problem by forming an equation where ...
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44 views

Finding the distance between two moving objects

In this case there is a missile whose initial position is $A(30,40)$ with a velocity of $[50,30]$ and an asteroid whose initial position is $B(400,250)$ with a velocity of $[-20,-30]$. The position of ...
0
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1answer
43 views

Kernel of a polynomial

Let's say we have a 2nd degree polynomial $a+bx+cx^2$ and it is given that $T:P2\rightarrow R$ given by $T(p)=\int_{0}^{1}p(x)dx$ We are asked to find the kernel of $T$. Now, I know that depending ...