# Tagged Questions

In $\Bbb R^3$, the cross product of two vectors $v$ and $w$ produces a vector $v \times w$ perpendicular to both. This tag is not meant for products in other mathematical contexts, such as products of groups (such as the [tag:direct-product]), sets (the Cartesian product), graphs, and so on.

69 views

### what is the difference between cross product and exterior product?

I have learn that the exterior product is an oriented plane called bivector given as $A \times B = |A||B| \sin x (i \times j)$ For $x \in(-\pi,\pi)$. I will like someone to derive the cross product ...
49 views

### How to solve proportions involving vector cross products?

I have the following proportion $\vec{JV} \times \vec{F_v} = \vec{JM} \times \vec{F_m}$ and all members are known except the magnitude of the vector $\vec F_m$, like described by another question here ...
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 ...
32 views

17 views

### Edge Chromatic Number of Product Graphs

Assume that two graphs like $G$ and $H$ are given. $G \times H$ is a graph such that every vertex of it comes from $V(G) \times V(H)$ and every vertex like $(u,v)$ is adjacent to $(u',v')$ iff : $1$...
288 views

15 views

61 views

### Determining an unknown vector from its cross and dot product with known vector

Let $\vec{k}$, $\vec{v}$, and $\vec{u}$ be vectors, where $\vec{u}$ is unknown and $\vec{k}$ and $\vec{v}$ are known vectors. Given: $\vec{u}\cdot\vec{k}=c$ $\vec{u} \times \vec{k}= \vec{v}$ ...
25 views

### Find the magnitude/length of the cross product of two vectors [duplicate]

I'm going through past exam questions, and this is one I haven't come across. How can I approach it?
21 views

### Order of operations - cross product and simple multiplication [closed]

I'm just wondering which takes precedence or if it really matters. It would matter wouldn't it? For example, this is written in my textbook: Equation for magnetic field of a point charge so the [qv ...
30 views

### Scaling by Jacobian for cross product?

I am trying to show that if $X:U\to\mathbb{R}^3$ is a parametrization of a coordinate patch on a refular surface $S$ and $F:U'\subset\mathbb{R}^2\to U$ such that $Y=X\circ F$ is a regular ...
24 views

### Integrating a cross product by parts

I'm looking to integrate the following using something like integration by parts and am not exactly sure how to go about it/where to begin. $\int (w \times u) \cdot v$ Where $w= \nabla \times u$ ...
72 views

### Intuition behind cross-product and area of parallelogram

The cross product in 2D is defined like that: $|(x_1, y_1) \times (x_2, y_2)| = x_1 y_2 - x_2 y_1.$ I perfectly understand the first part of the definition: $x_1 y_2$, which is simply the area of a ...