Tagged Questions
0
votes
2answers
58 views
Computing cross product using norm and angle
Sorry for the weird title, if someone finds a better title for my problem be my guest to edit it ;)
For $\mathbf{v,w} $ in R³ with $\mathbf{||v||=1 ;||w||=4; \theta
=\frac{2\pi}{3}}$
Solve ...
1
vote
1answer
30 views
Find vectors vertical to given vectors with certain length
Given the vectors $\mathbf{u,v}$ in R³, determine all vectors that are
vertical to $\mathbf{u}$ and $\mathbf{v}$ with length = 1
Every vector $\mathbf{x'}$ that is to be found must meet these ...
1
vote
3answers
39 views
Reordering vector product
If I have vectors $a, b, c \in \mathbb{R}^3$, and if we have e.g. $a = b\times c$, is there any way to express $b$ in terms of the other two?
1
vote
1answer
51 views
Solution set to cross product
If $\vec a,\vec b \in \mathbb{R}^3$ with $|\vec a|\ne0$ show that the equation $\vec a \times \vec u =\vec b$ has a solution if and only if $a \cdot b = 0$ and find all the solutions in this case.
...
-4
votes
2answers
120 views
Why cross product's formulas defined in this way?
Why cross product's formulas defined in this way?
When mathematicians need to define cross product?
1
vote
1answer
46 views
Test of handedness
I'm reading a book on linear algebra, where the author gives a method to test the handedness or chirality of a given set of 3 basis vectors.
if (v1 x v2) . v3 > 0 then it's right-handed, while if ...
1
vote
2answers
55 views
Vectors and Cross Product
I have these two questions regarding the Cross Product.
1.) You are looking down at a map. A vector $u$ with $|u| = 3$ points north and a vector $v$ with $|v| = 10$ points northeast.
What is $|u ...
1
vote
1answer
80 views
How to generate an ordered list of vertices of a cube from a face and a normal vector
Consider a cube with faces we'll call "left", "right", "front", "back", "top" and "bottom".
The cube can be described by $0 \le x,y,z \le 1$.
To name the faces, we'll say $x$ extends to the right, ...
-1
votes
2answers
83 views
Find the sine sign given a pair of 3D vectors
I want to find the exact sine between two vectors in 3-dimensional space.
Data:
$x$: vector
$y$: vector
$z = \Vert x \times y \Vert$
I have tried this:
$$\sin \alpha = \frac{\Vert z\Vert}{( ...
9
votes
4answers
655 views
Is the vector cross product only defined for 3D?
Wikipedia introduces the vector product for two vectors $\vec a$ and $\vec b$ as
$$
\vec a \times\vec b=(||\vec a||||\vec b||\sin\Theta)\vec n
$$
It then mentions that $\vec n$ is the vector normal ...
2
votes
1answer
84 views
Vector question, solving $r\wedge a=b$ and $r\wedge c=d$, with conditions
I am stuck on the following
Show that the vector equation $r\wedge a=b$ has a solution $$r=\lambda a + \frac {a \wedge b}{|a|^{2}}$$
Show that the vector $r\wedge a=b$ and $r\wedge c=d$, with ...
2
votes
2answers
150 views
Vectors question
I'm trying to prove whether the followings statements are true or not. I would appreciate your help, as I'm not sure how to begin.
Given:
$ u,x_n \in \mathbb{R}^3$ and for every $n$, let $x_{n+1}=u ...
4
votes
1answer
391 views
Cross product of vectors as a determinant: valid matrix operation?
"The definition of the cross product can also be represented by the
determinant of a formal matrix."
—Wikipedia
This seems like a hack to me—something of much practical use but ...
