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December 28th, 2018, 09:08 PM   #1
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A vectorial calculation

Hello all,

Knowing $\displaystyle \overrightarrow{z}=\overrightarrow{x}+ \overrightarrow{y}$ to calculate $\displaystyle \overrightarrow{z}^n$ where the three vectors are not collinear , $\displaystyle n\in \mathbb N$ and $\displaystyle n\geq 2 $.

All the best,

Integrator

Last edited by Integrator; December 28th, 2018 at 09:29 PM.
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December 28th, 2018, 09:45 PM   #2
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what does $\large \vec{z}^n$ mean?
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December 29th, 2018, 01:26 PM   #3
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December 29th, 2018, 02:05 PM   #4
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The title of the thread is ”vectorial calculation”
Maybe n is an exponent
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December 29th, 2018, 03:24 PM   #5
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Originally Posted by idontknow View Post
The title of the thread is ”vectorial calculation”
Maybe n is an exponent
Yeah, but the only way to do that is to use the cross product. It's going to get messy. I'm not sure that is what the OP is trying to do.

-Dan
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December 29th, 2018, 06:11 PM   #6
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Yeah, but the only way to do that is to use the cross product. It's going to get messy. I'm not sure that is what the OP is trying to do.

-Dan
not to mention that $\vec{v} \times \vec{v} = \vec{0}$
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December 29th, 2018, 08:51 PM   #7
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not to mention that $\vec{v} \times \vec{v} = \vec{0}$
Heloo,

This is a trivial case....The scalar product $\displaystyle \overrightarrow {v}^n=\overrightarrow{v} \cdot \overrightarrow{v} \cdots
\overrightarrow{v}\cdot \overrightarrow{v}$ is what would be interesting to calculate.

All the best,

Integrator
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December 29th, 2018, 10:00 PM   #8
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Quote:
Originally Posted by Integrator View Post
Heloo,

This is a trivial case....The scalar product $\displaystyle \overrightarrow {v}^n=\overrightarrow{v} \cdot \overrightarrow{v} \cdots
\overrightarrow{v}\cdot \overrightarrow{v}$ is what would be interesting to calculate.

All the best,

Integrator
this post shows you have no idea what you're talking about.

$\vec{v}\cdot \vec{v}$ is a scalar and thus cannot be further dotted with a vector.

Please stop wasting everyone's time.
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December 30th, 2018, 02:58 AM   #9
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A relevant product would be the geometric algebra product, which for vectors equals

$$\overrightarrow{v}\overrightarrow{w} = \overrightarrow{v}\cdot \overrightarrow{w} + \overrightarrow{v}\times \overrightarrow{w},$$
the sum of cross and dot product. But to compute further and take the $n$th power of a vector, you'd need the formula for the geometric algebra product for arbitrary blades, and that's pretty ugly.
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December 30th, 2018, 09:47 PM   #10
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Quote:
Originally Posted by Micrm@ss View Post
A relevant product would be the geometric algebra product, which for vectors equals

$$\overrightarrow{v}\overrightarrow{w} = \overrightarrow{v}\cdot \overrightarrow{w} + \overrightarrow{v}\times \overrightarrow{w},$$
the sum of cross and dot product. But to compute further and take the $n$th power of a vector, you'd need the formula for the geometric algebra product for arbitrary blades, and that's pretty ugly.
Hello,

The problem I posted is from another forum...It is known that if $\displaystyle \overrightarrow{z}=\overrightarrow{x}+ \overrightarrow{y}$ , then $\displaystyle \overrightarrow{z} ^2=\overrightarrow{x}^2+\overrightarrow{y}^2+2 \overrightarrow{x}\overrightarrow{y}$ and so what expressions do they have $\displaystyle \overrightarrow{z} ^3$ , $\displaystyle \overrightarrow{z}^4$ , $\displaystyle \overrightarrow{z}^5$ ,......., $\displaystyle \overrightarrow{z}^{n-1}$ , $\displaystyle \overrightarrow{z}^n$?
Thank you very much!

All the best!

Integrator
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