# 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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### Cross product word problems do not make sense to me in textbook [closed]

I'm having trouble following both of these examples.  In 4, I can't figure out what is going on? What is the moment of force? What is the moment of the force p about the center Q of a wheel? What is ...
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### Find all functions f(t) such that x = (cost, sint, f(t)) is a plane curve

Okay so I have a question How do we find all function f(t) such that x = (cost, sint, f(t)) is a plane curve I know this means the torsion is 0. So I know that we can find the pieces of the TNB needed ...
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### Is there a 'geometric' version of this derivation of the vorticity equation?

Recall that for each vector $\omega\in\mathbb R^3$, there is an anti-symmetric matrix $[\omega]_\times\in\mathbb R^{3\times 3}$ (and vice-versa) such that $$[\omega]_\times h= \omega\times h.$$ ...
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### How to get the 3 points that are collinear in 3 different line equations with a common variable?

So I already have 3 defined equations that give me 3 different lines, two of which are curved. Doesn´t matter how I got them, they are right. They are simply a vector plus another vector multiplied by ...
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### Why is the derivative of of the unit tangent vector a cross-product?

Equation for T(t) Equation for curvature Alternate curvature equation Using the equation for T(t) and the equatian for curvature, how does the quotient rule when solving for dT/dt become a cross-...
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### How can I prove $[r][\omega]^{2}r = -[\omega][r]^2\omega$?

A derivation I am reading from a book requires me to prove $[r][\omega]^{2}r = -[\omega][r]^2\omega$ . Now this was part of a larger derivation and hence the book skipped a few intermediary steps and ...
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### Finding a general equation of a plane

Let $x = [3, 4, 2], y = [2, −1, 3],$ and $z = [−1, 2, 1]$. Give a general equation of the plane $P$ in $\mathbb{R}^3$ which passes through the point $[1, −2, 2]$ and has direction vectors $x$ and $y$. ...
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### If a.i=4, then ,what is the value of (axj).(2j-3k) , where a is a vector

This is a question I saw in a question paper of a competitive exam but I was unable to solve it. Can anyone please assist me with any sort of hint to solve this problem and any type of explanation if ...
How would one go about resolving the vector $\vec{p}$ into parallel and perpendicular vectors to the given vector $\vec{w}$ By considering - $\vec{w}\times(\vec{p}\times\vec{w})$ So far I have ...