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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Want to get knowledge about vector

"Basically, when we multiply 2 by 3, we get 6. Here, 3 times 2 equals 6. Similarly, when we multiply vector A by vector B, we might expect to get AB. However, instead of AB, we get AB times ...
shanto khan's user avatar
2 votes
0 answers
47 views

Does the eigenvectors for the sum of projections onto unit vectors that sum to zero imply a symmetry of the set of unit vectors?

I am interested in a sum of projectors $A = \frac{\text{Tr}(A)}{N}\sum_{i=1}^N \mathbf{a}_i\,\mathbf{a}_i^T$, where $N$ is the total number of unit vectors, $\mathbf{a}_i$ is a real column vector with ...
Luzveraz's user avatar
3 votes
1 answer
67 views

Difficulty understanding why dot product is necessary in solving the angle between line and a plane

A line with equation $L = (1, 0, -2) + s(2, -1, 2)$ intersects with the plane $x + 2y + z = 2 $ at an angle of $\theta$ degrees. I am having some difficulty understanding why the dot product is ...
sesandc3123's user avatar
-3 votes
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41 views

Numerical analysis - matrix [closed]

My matrix: 3 -1 1 = 6 -2 5 3 = -22 3 -3 5 = 20 I couldn't figure out how to solve the exercise and would appreciate an answer Find a pair of vectors ...
derey yovel's user avatar
2 votes
1 answer
52 views

Confirming the angle between intersecting planes using projections

Let's say I have 2 planes: $$\text{Plane}_1: x + 2y - z = 3$$ and $$\text{Plane}_2: 2x -y +3z = 4$$ which have normal vectors of $[1,2,-1]$ and $[2,-1,3]$ respectively. It's clear that the normal ...
achacttn's user avatar
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Tangent vectors to regular curve at constant angle to a fixed vector

Problem: Show that the tangent vectors to the regular curve $x(t)=(3t,3t^2,2t^3)$ make a constant angle ($\theta$) with the vector $a:=(1,0,1)$. We have $b:=x'(t)=(3,6t,6t^2)$. I worked out that $b\...
Alex Petzke's user avatar
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Tangent Vector, Principal normal vector, Binormal vector, and Torsion

So I'm trying to fully grasp how all these relate. My current understanding is that the tangent vector describes the direction in which the curve is going/curving. Meanwhile, the principal norm is ...
A Student 's user avatar
-1 votes
1 answer
37 views

Are any 2 linear combinations of a set of linearly dependent vectors linearly dependent?

I am trying to prove whether the following statement is true or not: that if we have some linearly dependent vectors, any 2 linear combinations of these vectors constitutes a linearly dependent set ...
Princess Mia's user avatar
  • 2,433
-3 votes
1 answer
51 views

Angle between b and c is θ and a×(a×b) = c. Find Tan θ [closed]

I am really confused about how I should proceed with this question Let a, b and c be the three vectors having magnitudes 1, 5 and 3 respectively, such that the angle between b and c is θ and a×(a×b) =...
Aakash Mutum's user avatar
6 votes
1 answer
140 views

Confusion regarding vector/matrix multiplication in index notation

I came across this question and answer (sorry I don't have an electronic source for it, only a paper copy). After reading the answer it had me questioning the notation one uses to denote row/column ...
digital's user avatar
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Is it possible to add a 3rd dimension to the Spectre Tiles (once reviewed)? [closed]

Spectre Tiles are referenced in Einstein's Problem Wikipedia Page Is it possible to add a 3rd dimension to the Spectre Tiles? P.S. help adding the appropriate tags ( i have not idea ) on this ...
htfunny's user avatar
-1 votes
0 answers
19 views

Calculate displacement of object when rotated [closed]

I’m a computer science student but I think I have a physics problem I need help with. We have a device and team is attempting to calculate the vertical displacement. In other words, it moves up and ...
user avatar
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Simple-ish grad question: grad of field of arbitrary dimensions

I'm doing problem set #0 from Stanford's CS229 course. They asked a pretty simple question: what is $\nabla f(x)$ where $f(x)=\frac{1}{2}x^TAx+b^Tx$, $A$ is symmetric, and $b$ and $x$ are vectors? I ...
CodeStacker42's user avatar
2 votes
2 answers
100 views

Find equation of plane using a system of equations

I need to find the equation of a plane $\alpha$ which is parallel to the line:$$ l: \begin{cases} x = -2 + t\\ y = 3 + t\\ z = 4 - t \end{cases} $$ and the line $g$ lies on the plane:$$ g: \begin{...
programk5er's user avatar
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Question regarding minimum time taken to move a point onto a line joining two points

This question is regarding the following problem A bird is at a point $P(4, –1, –5)$ and sees two points $P_1(–1, –1, 0)$ and $P_2(3, –1, –3)$. At time $t = 0$, it starts flying with a constant speed ...
koiboi's user avatar
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Line integral of a vector field over a closed path [closed]

Let $f(x,y,z)=(y,x,x)$ be a vector field. Then it can be shown that $f$ is not a gradient. Find a closed path in $\mathbb{R}^3$ such that the integral of $f$ over that part is non-zero. Regarding ...
Mathguide's user avatar
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2 votes
1 answer
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Calculating angle of 3D vector.

I am trying to make a program to calculate the ground track of a satellite around the Earth. I have got stuck trying to finding the angle of the ground track relative to the equatorial plane. In the ...
KDP's user avatar
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1 vote
2 answers
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Question regarding meaning of resultant of two vectors

I just learnt about the following formula to compute the resultant of a 2 vectors $\vec{a} \text{ and } \vec{b}$. $$|\vec{a} \pm \vec{b}| = \sqrt{|\vec{a}|^2 + |\vec{b}|^2 \pm 2|\vec{a}||\vec{b}|\cos(\...
koiboi's user avatar
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Is this the correct equation for divergence of a horizontal vector field in spherical coordinates?

There is a Horizontal vector field $\textbf{V} = <u\hat{\lambda}+v\hat{\theta_{lat}} + 0\hat{\textbf{r}}>$ which is gridded along Earth's surface. Physically speaking, the vector field's ...
Researcher R's user avatar
0 votes
0 answers
21 views

Effect of Basis Change on Absolute Vector Magnitudes

Does Basis Change Affect the Absolute Magnitude of Vectors? How does a change in basis impact the absolute length of vectors? I'm trying to understand the effect of a basis change on the absolute ...
fatFeather's user avatar
1 vote
1 answer
35 views

Analytical Method for Finding the Closest Point on a 3D Quadrilateral Polygon Face from a Line Segment

I am interested in developing an analytical method to determine the closest point on a convex quadrilateral polygon face, defined by four points (A, B, C, and D), from a given line segment connecting ...
Thinesh's user avatar
  • 13
-2 votes
0 answers
53 views

Minimizing Distance Between Vectors Through Linear Transformation

I'm working with two vectors, $Y$ and $X$, and I have to find a approximation for $Y$ using a linear transformation of $X$. I'm looking to find scalars $a$ and $b$ that minimize the distance between $...
Peyman's user avatar
  • 693
6 votes
2 answers
277 views

Is a scalar presented as a matrix or not here?

In the linear algebra course I am taking, the inner product of 2 vectors $\langle u, v \rangle$ is defined as being a scalar; however, it is also viewed as being a product of 2 matrices as $u^Tv$, as ...
Princess Mia's user avatar
  • 2,433
6 votes
6 answers
239 views

Geometric argument for why $(\mathbf{x}-\mathbf{p}_1)\cdot (\mathbf{x}-\mathbf{p}_2) = c$ is a circle

Let $\mathbf{p}_1, \mathbf{p}_2 \in \mathbb{R}^2, c \in \mathbb{R}$. Then the equation $(\mathbf{x}-\mathbf{p}_1)\cdot (\mathbf{x}-\mathbf{p}_2) = c$ defines a circle with centre $\frac{\mathbf{p}_1 + ...
wolfe's user avatar
  • 121
1 vote
1 answer
22 views

Cross product limit with angular singularity

I am trying to verify whether $$\lim_{\Pi \rightarrow \Omega } \frac{(\Omega \times \Pi ) \times \Pi \cdot v}{ \|\Pi \times \Omega\|^2} $$ remains bounded. $v$ is a constant vector, I managed to get ...
Theo Diamantakis's user avatar
1 vote
0 answers
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How to describe Lorentz transformation with magnetic monopole?

We know without magnetic monopoles ,the Lorentz transformation will be: $\begin{aligned}\vec{E}'&=\gamma(\vec{E}+\vec{\nu}\times\vec{B})-\frac{\gamma^2}{\gamma+1}\frac{\vec{\nu}}{c}\bigg(\frac{\...
rookie's user avatar
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1 vote
1 answer
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How can an identical vector have a lower dot product value than two different vectors?

Given two vectors: $\mathbf{v}_1 = (2, 2)$ and $\mathbf{v}_2 = (3, 3)$: Since the dot product is one method for measuring the similarity between vectors, and given that $\mathbf{v}_1 \cdot \mathbf{v}...
Edmar Miyake's user avatar
0 votes
0 answers
22 views

how to find circle of curvature centre point

For this question I am asked to find the radius and centre-point of the circle of curvature for the following function: $−7.87e^{2.65x}$ I calculate the radius correctly with the formula: $R =\frac{...
reira osaki's user avatar
0 votes
1 answer
53 views

If $F(x)=(F_1(x),\dots, F_n(x))$, is always possible to find $F_i(x)=\min\{F_1(x),\dots, F_n(x)\}$?

Let $n\ge 2$, ($n$ finite) and $F:\mathbb R\to\mathbb R^n$ be a positive function, meaning that $$ F(x)=(F_1(x),\dots, F_n(x))$$ and $F_i(x)\ge 0$ for any $i\in\{1,\dots, n\}$. My question is: is ...
Physics user's user avatar
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0 answers
23 views

Interpretation of a vector quantity

Suppose we have a vector field $\vec{A}$ in $\mathbb{R}^n.$ The following “vector quantity”: $$(d\vec{r} \cdot \nabla)\vec{A}$$ looks strange perhaps, but when expanded is seen to be a simple quantity:...
Jbag1212's user avatar
  • 1,513
1 vote
1 answer
40 views

Angle of attack between surface and vector

I'm trying to make a simplified sailing ship simulation and want to get the angel-of-attack between a surface normal vector (representing a sail) and a vector (representing the wind velocity). The ...
Claudijo's user avatar
  • 113
-1 votes
1 answer
24 views

Cosine similarity magnitude vector

there is one thing I'm not sure about regarding cosine similarity. Does the magnitude of the vector matter? I think the answer is yes, especially if you look at the picture below where the word count ...
Moooz's user avatar
  • 3
0 votes
1 answer
31 views

Is there an algorithm for sorting points in a field based on sweeping a line through them at an arbitrary angle?

Given a set of coordinates on a euclidean plane, is it possible to sort the points by sweeping a line through them where the line might not be strictly horizontal or vertical? The inputs to the ...
phill2mj's user avatar
-1 votes
0 answers
32 views

If $V={v_{1},v_{2},...,v_{n}}$ is an orthogonal set, determine if $\sum_{i=1}^{n}\left\| v_{i} \right\|=\left\| \sum_{i=1}^{n}v_{i} \right\|$ [closed]

If $V=\{v_{1},v_{2},...,v_{n}\}$ is an orthogonal set, determine if $\sum_{i=1}^{n}\left\| v_{i} \right\|=\left\| \sum_{i=1}^{n}v_{i} \right\|$ is true or not. I don´t even know where to start. ...
gnzlama's user avatar
  • 31
1 vote
1 answer
24 views

Figuring out if an object is headed in the right direction at a crossing?

For a video game, I am trying to figure out whether the ship is headed to the right direction, that is, forward relative to the race direction as it's a racing game in 3 dimensions. Basically, the ...
Eric Cartman's user avatar
0 votes
1 answer
39 views

Expressing the diagonal of a matrix filtered by a vector

I am trying to extract the mathematical expression of creating a set of elements from the diagonal of a matrix, but after filtering by a vector. For example: Let $A$ be a $3 \times 3$ matrix, $\mathbf{...
Lane's user avatar
  • 5
0 votes
1 answer
39 views

Drawing tangent vector

this is the solution provided from my class lecture notes. I have a question related to the graph drawing. Based on the calculation, we have two vectors, vector r(2) = <2,4> and vector r'(2) = &...
Woshi's user avatar
  • 133
0 votes
0 answers
16 views

Discrepancy Between Predicted and Observed Impact of Parameter Change in Multivariable Equation

Given: $$ \mathbf{a} = [a_1, a_2] \quad \text{and} \quad \mathbf{b} = [b_1, b_2] $$ The expression for $\mathbf{c}$: $$ \mathbf{c} = 3\mathbf{a}^3 - \mathbf{b}^2 $$ We need to find the partial ...
joaovitor_zz's user avatar
1 vote
0 answers
22 views

Torsion for a 3D curve can be positive or negative, while curvature is always taken to be positive. Why?

$$\frac{dB}{dS} = -\tau N = \tau(-N)$$ $$\frac{dT}{dS} = \kappa N$$ where $\tau$ is the torsion and $\kappa$ is the curvature. $\frac{dT}{dS}$, by convention, is defined to be in the direction of $N$, ...
Sasikuttan's user avatar
0 votes
0 answers
44 views

Deriving the Maximum Range of a Particle With A Constant Force Using Geometric Algebra

I am learning Geometric Algebra by reading New Foundations for Classical Mechanics, by David Hestenes. Chapter 3-2 studies the motion of a particle with constant gravitational force and on page 129 ...
Cereza's user avatar
  • 1
1 vote
0 answers
26 views

Find the coordinates of a vector product in an affine coordinate system

Let $\vec{OA}=\vec{a}, \vec{OB}=\vec{b}$ and $\vec{OC}=\vec{c}$ and $|\vec{a}|=3, |\vec{b}|=2$ and $|\vec{c}|=4$. We also know that $\measuredangle(\vec{a},\vec{b})=\measuredangle(\vec{a},\vec{c})=\...
Math Student's user avatar
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0 votes
0 answers
18 views

Meaning of $e_{1}$ in $|(s-e_{1})´v|=||s-e_{1}||\cdot ||v||$

(Sorry for any misspelling or gramatical error, I´m not a native english speaker) I am trying to solve this problem: Vector $u=\begin{bmatrix}a &a &a &b \end{bmatrix}´$ can be written as ...
gnzlama's user avatar
  • 31
-3 votes
1 answer
46 views

Hexagon Consisting of Complex Numbers [closed]

In the Argand plane, the points Q and A represent the complex numbers 4+6i and 10+2i respectively. If A, B, C, D, E, F are the vertices, taken in clockwise order, of a regular hexagon with centre Q, ...
Slavaaus's user avatar
0 votes
1 answer
26 views

projection of vector not equal length of the projection

I have 2 vectors, a and b, from the origin to a plane. The normal vector to the plane, is n. (a dot n) and (b dot n) is the same, and I learned it is equal to the projection of a onto n (and b onto n)....
trogne's user avatar
  • 129
0 votes
0 answers
17 views

Symplifying a cost function of an optimization problem

Background I have a zero-mean dataset $D(\theta)$ composed by $m$ vectors $y_{1}(\theta)$, $y_2(\theta)$, $\dots$, $y_{m}(\theta)\in \mathbb{R}^2$. Each observation $y_i(\theta)$ depends on a unknown ...
matteogost's user avatar
2 votes
1 answer
47 views

How to find the number of possible planes equidistant from $5$ points $3$ of which are collinear.

$\vec a,\vec b,\vec c,\vec d$ are four non zero vectors and points $P(\vec a), \; Q(\vec a+\vec b+\vec c), \; R(\vec a-\vec b-\vec c), \; S(\vec d),\; T(\vec a +\vec d)$ are distinct points such that ...
Skdmg's user avatar
  • 704
1 vote
1 answer
26 views

Inner Product of Error Vector and Residual Vector

I have that $A$ is a positive definite matrix and $b$ is some fixed vector. Define $r=b-Ax$ to be the residual vector and $e=A^{-1}b-x$ to be the error vector for all vectors $x$. I need to show that $...
slaint1027's user avatar
1 vote
1 answer
45 views

Can I always find two new linear independent vectors whose dotproduct with existing vector $\ge$ 0 in vector space $R^4$

suppose V is 4-dimensional vector space, $v_1$ and $v_2$ are linear independent in V, now for arbitrary plane S that goes through origin, can I find two new linear independent vector in plane S that ...
femto's user avatar
  • 367
1 vote
2 answers
42 views

The linear relationship between two plane(or two subspace)

Suppose $V$ is a $3$-dimensional vector space, suppose I have $2$ planes $S_1$ and $S_2$ going through the origin, then they must at least intersect at a line. Suppose $V$ is a $4$-dimensional vector ...
femto's user avatar
  • 367
2 votes
2 answers
113 views

Difficult Vectors Problem (Calculus & Vectors)

Find parametric equations of a line that intersects line 1 and line 2 at right angles. Line 1: $[x,y,z] = [4,8,-1] + t[2,3,-4]$ and Line 2: $[x,y,z] = [7,2,-1] + k[-6,1,2]$. I've tried solving this ...
math's user avatar
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