Use this tag for questions involving vectors, quantities that have magnitude and direction.

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0answers
18 views

DFT of vector $(0, 1, 2, 3)$

The problem is that my answer is different from answer i get in MATLAB. My answer is $(6, -2-2i, -2, -2+2i)$ while MATLAB answer is $(6, -2+2i, -2, -2-2i).$ In MATLAB i use command ...
0
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1answer
17 views

Space formed by dot products of three vectors

Suppose I have 3 3D unit vectors $\mathbf{v}_1$, $\mathbf{v}_2$, and $\mathbf{V}$. I define the three corresponding scalars $u_1=\mathbf{v}_1 \cdot \mathbf{V}$, $u_2=\mathbf{v}_2 \cdot \mathbf{V}$, ...
-1
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1answer
24 views

Show that the midpoint of $AB$, $AC$, and $DE$ are aligned.

Let $ABC$ be a rod, $D$ and $E$ two points such as: $\vec{EC} = k \cdot \vec{EA} / \vec{DA} = k \cdot\vec{DB}$. How can I show that the midpoint of $AB$, $AC$, and $DE$ are aligned?
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2answers
20 views

Connecting the scalar triple product with the intersection of two lines?

There are two lines r=a+tu and r'=b+t'v, where t and t' are scalars. Show that if they intersect, then [v,b,u]=[v,a,u]. I've tried finding the intersection between the lines and working from there, ...
1
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1answer
17 views

Airplane Wind problem

Airplane flying at 400 mph at an angle of 30 deg encounters a wind. The resultant velocity of the airplane is 475.3 mph at an angle of 27.18 deg. What was direction of the wind. I set this up as ...
1
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0answers
28 views

Second derivative of the position vector in a spherical coordinate system

In a spherical coordinate system my unit vectors are: $\vec{e_r}=\begin{pmatrix}\sin\theta\cdot \cos\phi \\ \sin\theta \cdot \sin\phi \\ \cos\theta \end{pmatrix}$; ...
1
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1answer
32 views

Calculate the viewing-angle on a square (3d-calc)

I'm in big trouble: My program (Java) successfully recognised a square drawn on a paper (by its 4 edges). Now I need to calculate, under which angle the webcam is facing this square. So I get the 4 ...
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2answers
27 views

Describe geometrically the set of solutions to the following equations in 3-space

Given $a, b \in \mathbb{R}^3$ and $\lambda \in \mathbb{R}$ I'm looking to describe, geometrically, the set of all $x \in \mathbb{R}^3$ satisfying both equations $a\cdot x = \lambda$ $a \times x = b$ ...
1
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0answers
32 views

Difficult Vectors Question

The variable line $l_1$ passes through the point $A$ $(2, 1, -1)$ and is parallel to the direction $ti + j +(1-t)k$ The variable line $l_2$ passes through the point B(1, -2, 3) and is parallel to the ...
3
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1answer
25 views

Splitting a vector into two axis aligned vectors

I'm not familiar with mathematical terms, so I'll try my best to explain this issue. Also, I don't know if this is a programming question or a mathematical one. I guess both... I'm making a 2D ...
1
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1answer
18 views

Derivative of vector valued function

The following is given for $ ∂x^TAx/∂x $ in a book on Matrix Algebra: What I cannot understand is: Where does $A^T$ come from in the second row (in the term $ ty^TA^Tx $)?
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3answers
42 views

Why does the determinate definition of the cross product give a vector that is perpendicular to the plane?

I'm trying to understand what a cross product really is. From what I can tell, the length of $\mathbf a \times \mathbf b$ is a measurement of how much $\mathbf a$ and $\mathbf b$ are NOT moving ...
0
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1answer
23 views

Gram-Schmidt process in function subspace

I have a function space $\mathcal {F}([-1,1],\mathbb R)$ and the subspace $\mathcal{P_2}:=$ $(x\mapsto a_o+a_1x+a_2x^2| a_0,a_1,a_2 \in \mathbb R )$ for all polynomials with degree $\le2$. In this ...
1
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1answer
31 views

Vector question involving an operator!

So, here's the problem: An operator H capable of operating on vector x, is defined in terms of a given vector a by: H x=(a * x) where $*$ representes vector product Given that ...
1
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1answer
31 views

Why is the “Normal Vector” normal?

I was trying to understand why the unit normal vector is normal to the direction of motion. Note that $\mathbf T(t) = \frac{\mathbf r'(t)}{||\mathbf r'(t)||}$ is the unit tangent vector for some ...
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3answers
35 views

When is this vector valued function pointing towards the origin?

"A fighter plane, which can shoot a laser beam straight ahead, travels along the path $\mathbf{r}(t) = \langle 5 - t, 21 - t^2, 3 -\frac{1}{27}t^3\rangle$. Show that there is precisely one ...
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1answer
57 views

Given two points and two normals, how to find third point

I really don't know how to search for this specific question. So, I'll try my best to explain my issue. I have the point P1 (pink) and the normal vector M (white) of its line, Given an ...
4
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3answers
44 views

Are $\vec{v}$ and $\vec{w}$ linearly independent?

Am I correct in saying that $\vec{v}=\begin{pmatrix}1\\2\\0\end{pmatrix}$ and $\vec{w}=\begin{pmatrix}2\\4a\\a-1\end{pmatrix}$ are linearly independent $\forall a\in\mathbb R$ /{1}? It seems to me ...
-1
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0answers
24 views

Jacobian from spherical coordinates [closed]

I have the following equations for a particle $$ \mathbf{p}=\left(\begin{array}{} p_x\\ p_y\\ p_z \end{array}\right)=\left(\begin{array}{c} E_{\mathrm{particle}}\cdot\sin\theta\cos\phi\\ ...
1
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1answer
20 views

Difference Between Dot Product and Scalar Projection?

I don't understand the difference between the dot product of two vectors and the scalar projection of a vector onto another one. To me it looks like they are both (geometrically) the length of the ...
3
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2answers
32 views

Linear Algebra--searching a name for certain transformations

I am currently taking a Linear Algebra class in Spanish and having difficulty coming across the correct translation for what we are studying. I am looking at a question that asks for the rotation of ...
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4answers
49 views

Applying math knowledge [closed]

Currently I'm in the middle of my first year of college studying informatics engineering. I was never great at math, but if I put some effort, I understand it and constantly get good grades. However, ...
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2answers
16 views

Relation between position vectors of a rectangle

I am given the position vectors of the rectangle a,b,c,d. I am supposed to prove that a.c=b.d (.=dot product) I tried representing the adjacent sides in terms of a,b,c,d since their dot product is ...
2
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0answers
43 views

How to rewrite this trigonometric formula in terms of scalar and vector products between vectors?

Given two angles $\alpha$ and $\gamma$ such that $$ \cos(\alpha) = v\cdot v' $$ and $$\cos(\gamma) = f\cdot f',$$ what is the simplified form of $\cos(\alpha + \gamma)$ in terms of the vectors ...
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2answers
25 views

How to differentiate this position Vector $\vec r=\rho\vec e_\rho+z\vec e_z$

Given the unit vectors: $\vec e_\rho=\bigl(\begin{smallmatrix} cos(\theta )\\ sin(\theta )\\0 \end{smallmatrix}\bigr); \vec e_\phi=\bigl(\begin{smallmatrix} -sin(\theta )\\ cos(\theta )\\0 ...
2
votes
1answer
13 views

Area of a Parallelogram Using Vectors

I am not sure if I am doing this problem correctly. I need to find the area of the parallelogram whose vertices are the points $P(0,1,1), Q(1,2,1), R(2,4,1), S(3,5,1)$ So to find the area I need to ...
0
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2answers
16 views

Finding the tension in two ropes.

I have a problem that says to find the tension in two ropes in the following figure. The answers are 1830kg in the right rope and ...
0
votes
1answer
12 views

Demonstrate colinearity of two vectors in math exercise

I'm getting stuck with a part of my math exercise where I have to demonstrate the colinearity of two vectors without using the coordinates. Note: All the vectors I will show will not have their arrow ...
1
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2answers
21 views

Orthonormal basis in a cylindrical coordinate system

So I am supposed to show if these vectors make an orthonormal basis in a cylindrical coordinate system. $\vec e_p=\bigl(\begin{smallmatrix} cos(\theta )\\ sin(\theta )\\0 \end{smallmatrix}\bigr); ...
4
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3answers
553 views

Kernel Explanation

sorry for asking so many questions lately but our lecturer is doing a terrible job explaining things. Calculate $ker(A)$ given that: $f:\{\mathbb{R}^3→\mathbb{R}^3; r→ A\vec{r}\}$ $A= ...
0
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0answers
15 views

Searching for a definition for n-Dimensional rotation which is cosine-distance invariant

I am wondering if it is possible to define a rotation for an $n$-Dimensional space ($n=2,3,4,5,\dots$). Given any vector $\vec v$, and knowing that it should be rotated to ...
0
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0answers
48 views
+50

Identity of the pushforward of a vector field using a Jacobi bracket.

Let $Z(u,v)$ be the vector field $Z(u,v)=(u^2+u,v^2+v)$, let $\Gamma_t$ denote its flow. I have shown that $[X,Z]=Z-X$. Show that $(\Gamma_t)_*X=e^{-t}X-(e^{-t}-1)Z$. Could someone please show me ...
1
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4answers
43 views

Why is this a valid definition of the dot product?

$(\vec{u},\vec{v})=u_1v_1+2u_2v_2+3u_3v_3$ I have never seen this definition before. I am used to the dot product looking something like this: $(\vec{a},\vec{b})=a_1b_1+a_2b_2+a_3b_3$ Where do the ...
0
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1answer
7 views

Suppose that the following two vectors u and v are perpendicular. Write the number b in terms of a.

Q) Suppose that the following two vectors u and v are perpendicular. Write the number b in terms of a. $$u=\begin{pmatrix}2 \\-2 \\\end{pmatrix}$$ and $$v=\begin{pmatrix}a \\b \\\end{pmatrix}$$ ...
0
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1answer
30 views

Yet another n-Dimensional Rotation question: is there a definition for n-Dimensional rotation which is cosine-distance invariant? (TO CLOSE)

(Moved to Searching for a definition for n-Dimensional rotation which is cosine-distance invariant, flagged it to delete it) I'm wondering if there exists a rotation definition by which the vectors ...
0
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2answers
22 views

express vector with other vectors

I have 4 vectors, A(2,2,2), P(2,3,4), Q(3,−1,0), R(-4,-1,-3). I found that they are linearly independent. The next question is to express A vector with other vectors.
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2answers
16 views

Intuition for using vectors in sale related problems

I am reading Linear Algebra from David Lay's book. He gives one example to showcase use of linear combination of vectors : I understand the solution, but I am completely clueless about how to ...
0
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1answer
32 views

Matrix addition

How do I solve the following? [2x1 -3x2 + x3; 4x1 - 2x3] + [x1 +2x2; 0x1 - 2x2; 4x1 + x2]^T When I do the transpose of the second matrix and try to add them together I get lost. Should I consider x1 ...
0
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1answer
21 views

Magnitude of vector $\vec{v}$? [closed]

The initial is $(-6,1)$ and the terminal is $(2,5)$. I was just wondering how to find the magnitude.
0
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1answer
13 views

Magnitude and direction angle?

What is the magnitude and direction angle of $v=4i+4j$? I have no idea how to start this problem, so any hints/formulas/tips and tricks would be useful, thank you!
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2answers
19 views

Find the projection of $U$ onto $V$?

I'm really stuck on this precalc problem: Find the projection of $u$ onto $v$ if $u=(-3,3)$ and $v=(-2,5)$.
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1answer
58 views

Simplifying the sum $\sum\limits_{i=1}^n\sum\limits_{j=1}^n x_i\cdot x_j$

How can I simplify the expression $\sum\limits_{i=1}^n\sum\limits_{j=1}^n x_i\cdot x_j$? $x$ is a vector of numbers of length $n$, and I am trying to prove that the result of the expression above is ...
0
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3answers
49 views

$\vec{r} \times (\vec{\omega}\times \vec{r})=r^2\vec{\omega}-(\vec{\omega}\cdot\vec{r})\vec{r} $

Show (in cartesian coordinates) that $\vec{r} \times (\vec{\omega}\times \vec{r})=r^2\vec{\omega}-(\vec{\omega}\cdot\vec{r})\vec{r} $ I am not really sure how to calculate this. Do I just assume ...
0
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1answer
18 views

How do I get the start and endpoint of a line using the middle point and the angle?

I have a line that goes from P1 to P2 in a 2D space. I have the location of the middle point of that line, and the angle of inclination of the line. The thing is that I don't know the length of the ...
1
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1answer
23 views

Taking the Derivative: Power Rule with Respect to Vector

I'm trying to take the derivative of \begin{equation} \phi\left(\mathbf{x}\mathbf{\theta}\right)\mathbf{x}^{\top} ...
1
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1answer
48 views

Can the equation $\mathbf{Av}=\mathbf{b}$ be solved as $\mathbf{v}=\mathbf{A}^{-1}\mathbf{b}$?

Say I have a $3\times 3$ matrix called $\mathbf A$ and a column matrix vector $\mathbf v$ and another column matrix vector $\mathbf b$. If I have the equation $\mathbf{Av}=\mathbf{b}$ where I know ...
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0answers
16 views

Comparing error vectors from different dimensions

I lack proper mathematical jargon, so pardon me in advance. Imagine a software application that generates error vectors. The error vectors are bounded between 0 ...
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1answer
33 views

Prove that a function is a linear transformation.

Lets say that I have a vector space $A$ and a linear transformation defined as $f : A → A$. Now I have a function $g : A → A$ defined as $g(a) = bf(a)$ where $a\in A$ and $b \in \mathbb{R}$ is a ...
0
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1answer
26 views

How to find the equation of a hyperplane in $\mathbb R^4$ that contains $3$ given vectors

Find the equation of a hyperplane in $\mathbb R^4$ that contains $3$ given vectors. The vectors are: $$v_1 = (1,0,-1,0),\quad v_2 = (0,1,1,1),\quad v_3 = (1,1,-1,0) $$ I've found the equation ...
0
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0answers
28 views

Split a vector into three

Say we have a vector of length n<100, $v(w_1,w_2,\ldots,w_{n})$. My problem is to divide the vector $v$ into groups of $3$, eg $u_m =(w_i, w_k, w_k)$ with as close weight as possible. Eg to ...