# Questions tagged [cross-product]

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.

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### Magnitude of torque due to weight in a simple pendulum

Suppose we have a simple pendulum as shown in figure . In this frame, suppose we fix $\theta$ as positive if rotation is at right of axis of symmetry (as depicted in figure) and negative if rotation ...
1 vote
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### How to intuitively understand cross-product

I have learned about the cross-product of vectors in both mathematical studies and physical ones but I am still curious as to how one can obtain an intuitive understanding of how two vectors create a ...
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### Establishing a new coordinate sytem in a plane defined by 4 points

Suppose I am given 4 points in 3D in the global coordinate system [X,Y,Z]. Now, I would like to establish a new coordinate system [x',y',z'] such that o' is in the center of the plane defined by the ...
1 vote
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### Getting a wrong result while computing the cross product of unit vectors $\hat{i}$ and $\hat{j}$

Consider the coordinate system as shown below and unit vectors along x and y, $\hat{i}$ and $\hat{j}$. The cross product of these unit vectors as given here is equal to $\hat{k}$. However, when I ...
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### Cross product implying vectors are equal [closed]

For 3-D vectors $a$, $b$ prove: $a \times b = a − b$ implies $a = b$ I've been working on this question for a while and have no idea how to solve it, any help would be greatly appreciated, thanks.
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### How does an almost complex structure on a sphere determine a 1-fold cross product?

In the article "VECTOR CROSS PRODUCTS ON MANIFOLDS", by Alfred Gray, the author states, between theorem 2.8 and corollary 2.9, that The existence of vector cross product of Type I [1-fold ...
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### Relationship between cross-product and Moore-Penrose pseudoinverse [closed]

It is said in here https://blog.bham.ac.uk/intellimic/g-landini-software/colour-deconvolution-2/ that you can get the third vector of a 3x3 (stain) matrix either by taking the cross product of the ...
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### Area of a parallelogram spanned by two 4D vectors without using trigonometry

In 3D, we can find the area of the parallelogram spanned by two vectors by using the cross product: $$Area = {\vert\vec a \times \vec b\vert}$$ In 2D, we can perform a similar operation using a 2D ...
1 vote
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### inverse action of cross product

Suppose we have two vectorsfield A(x,y,z) and B(x,y,z).If we know B = (0,2,1) can we compute A if: ? EDIT: After some searching online I found that there are infinitely many vectors fields A(x,y,z) ...
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### Normal vector to a plane containing the Origin

The points A,B,C have position vectors; 2i+2j, -j+k and 2i+j-7k respectively, relative to the origin. Find the normal vector to the plane OAB. I know that $$\vec {OA}$$ and $$\vec {OB}$$ are in the ...
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### An example of integral with cross product

Suppose I have a uniform vector field ${\mathbf{f}}({\mathbf{x}}):\mathbb{R}^3 \to \mathbb{R}^3$. Let us fix a cylindrical coordinate system such that ${\mathbf f}({\mathbf x})=f\,\hat z$, where $f$ ...
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### Where did I go wrong computing the cross product

If $u=(-2,0,\sqrt2)$ and $v=(0,-4,-\sqrt2)$, then $u\times v=(2\sqrt2,-\sqrt2,8)$. I got $(4 \sqrt2, 2\sqrt2,0)$ for the cross product but the answer is saying I'm wrong and I don't know why