Questions tagged [vectors]

Question 1

I am trying to get a better grasp of how to find the basis of the tangent space. Here is one example I worked on in hopes of practicing it: Consider the chart $(U,\psi)$, the manifold $\mathcal{M} = S^...

Question 2

I have $n$ unit vectors $\mathbf{x}_i \in \mathbb{R}^p$, whose (sample) mean direction is calculated with $$ \mu = \frac{\bar{\mathbf{x}}}{\bar{R}}, \text{ where } \bar{\mathbf{x}} = \frac{1}{n} \...

Question 3

You're given two lines in the $xy$ plane, let's say $ Line 1: a_1 x + b_1 y + c_1 = 0 $ and $ Line 2: a_2 x + b_2 y + c_2 = 0 $ In addition you're given two points $P = (p_1, p_2) $ and $Q = (q_1, q_2)...

Question 4

You're given $\triangle ABC$ with known vertices in the $xy$ plane. The coordinates of $A,B,C$ are known. Now, given three distances $d_1, d_2, d_3$. You want to determine all congruent triangles $\...

Question 5

I am working on a special type of problem which requires that a vector field derived from previously computed fields satisfy 2 constraints: $$1) \oint \textbf{V} \cdot \hat{\textbf{n}} ds = 0$$ $$2) \...

Question 6

If I have two vectors $\vec{A}$ and $\vec{B}$ having two components I can calculate their scalar product. And then $\frac{\vec{A}\cdot\vec{B}}{||A|| \times ||B||}$ gives me their cosine, and through ...

Question 7

I believe that on an orthogonal coordinate system $(O,\vec{i},\vec{j})$, where $(O,\vec{i})$ would design the East, if someone gives me a single vector $\vec{R}(7.6, -3.4)$ it be convenient if I ...

Question 8

Given a unit vector $u$ and another unit vector $v$, I want to rotate $u$ into $v$ in two stages. In the first stage, I rotate $u$ about a given axis $a_1$ (by an unknown angle) to produce a vector $...

Question 9

In my school module it is written that the cartesian equation of $x$ axis is $$ \frac{x}{1}=\frac{y}{0}=\frac{z}{0} $$ Isn't dividing by zero not allowed? How have they written this equation

Question 10

Let two 3D unit vectors $V, V'$ be given. Derive vector $W$ created by clockwise rotating $V'$ by angle $\theta'$ around the origin within the plane with normal proportional to $V \times V'$. I tried ...

Question 11

Let there be two different points $ \vec{p_1}, \vec{p_2}$ on a unit sphere. I need to get unit vector $\vec{t}$ at the point $\vec{p_1}$ tangent to the meridian (big circle) connecting these points. ...

Question 12

I'm looking for a simple algebraic derivation of the cross product formula: $\vec{a} \times \vec{b} = \|\vec{a}\| \|\vec{b}\| \sin(\theta) \vec{n}$. I need the derivation to be simple, understandable ...

Question 13

I have this problem that I have been working on today. I want to calculate the local direction of the great circle connecting Ottawa, Canada, and Sarajevo, Bosnia. I assume Earth is perfectly ...

Question 14

On a plane, give a line $d$ and the vectors $\overrightarrow{u}, \overrightarrow{v}\ne\overrightarrow{0}$ such that $\overrightarrow{u},\overrightarrow{v}$ are not perpendicular to the line $d$. Let $...

Question 15

My beliefs: At school, I've seen all the time definition of vectors in $\mathbb{R^n}$. I've understood that if some are defined in $\mathbb{R^3}$ it means that: they all have three components all of ...

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Questions tagged [vectors]

Confusion regarding Tangent Basis

Standard error of a mean direction

Determine the reflection line about which two points reflected will lie on two given lines respectively

Congruent triangle to a given one, with its vertices at specified distances from the original triangle vertices

How to adjust a vector so that both its net circulation and flux vanish?

From two vectors I can get the cosine of their angle. But how to get that angle value (looking at quadrant) if they have more than two dimensions?

When I consider a vector directly, or by its scalar product with $\vec{i}$ I don't receive the same angle measure

Rotating a unit vector to another vector using two consecutive axes

Cartesian equation of X axis [closed]

Rotate vector within plane by given angle

Vector tangent to meridian

Simple Algebraic Derivation of the Cross Product [duplicate]

Bearing angle of great circular arc between Ottawa Canada, and Sarajevo, Bosnia

Show that $pr_d(\overrightarrow{u}+\overrightarrow{v}) = pr_d\overrightarrow{u} + pr_d\overrightarrow{v}$

I don't believe me, $\overrightarrow{Marc}(1.80\ m, 71\ kg, 56\ y.o.)$ I'm a vector of $\mathbb{R^3}$. But of $\mathbb{R^{+3}}$ or better. Am I right?

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