# 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.

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### Orthogonal matrix over cross product

Is $Qa \wedge Qb = \pm Q(a \wedge b)$, where $a$ and $b$ are two unitary vectors in $E^3$ and $Q$ is an orthogonal matrix ??? Thanks
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### If u(t) = < sin 6t, cos 6t, t >and v(t) = <t, cos 6t, sin 6t >, find d/dt u(t) × v(t) . [closed]

Hi I have been stuck on this problem for forever and can't figure out what I did wrong. Thanks! I got: <-6sin(6t)^2 -cos(6t)+6cos(6t)^2 +6tsin(6t), 2t-6cos(6t)sin(6t)+6sin(6t)^2, 6cos(6t)^2 + ...
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### Volume of tetrahedron using cross and dot product

Consider the tetrahedron in the image. Prove that the value of the tetrahedron is given by $\frac16 |a \times b| \cdot c$ So far, what I did was I know volume of the tetrahedron is equal to the ...
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### Cross product in complex vector spaces

When inner product is defined in complex vector space, conjugation is performed on one of the vectors. What about is the cross product of two complex 3D vectors? I suppose that one possible ...
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### How to tidy up this Cross Product derivation?

Last week I wrote this answer. However, I don't feel it is complete. I make an arbitrary choice of unit vector perpendicular to u,v. But I can't see how to integrate this fact into the derivation. ...
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### Octonionic formula for the ternary eight-dimensional cross product

A cross product is a multilinear map $X(v_1,\cdots,v_r)$ on a $d$-dimensional oriented inner product space $V$ for which (i) $\langle X(v_1,\cdots,v_r),w\rangle$ is alternating in $v_1,\cdots,v_r,w$ ...
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### Normal to surface at point

I have this function: $F(x,y,z)=x^2−y^2−z^2+4$ where $z\ge 0,0\le x \le 2,0 \le y \le 2$. How can I find the normal at some point $P=(p_x,p_y,p_z)$? I have tried to calculate the derivatives of ...
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### 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 : $1$...
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### Interpretation of eigenvectors of cross product

If we fix a non-zero vector $\boldsymbol{v}\in\mathbb{R}^3$, then the linear map $\boldsymbol{x}\mapsto\boldsymbol{v}\times\boldsymbol{x}$ has trivial eigenvectors $\boldsymbol{x}_1=t\boldsymbol{v}$ (...