Skip to content Skip to navigation

Connexions

You are here: Home » Content » algebra lineal producto cruz

Navigation

Recently Viewed

This feature requires Javascript to be enabled.
 

algebra lineal producto cruz

Module by: javier lopez. E-mail the author

<TeXmacs|1.0.6>

<style|generic>

<\body>

kolman seccion 5.1 ejercicio numero 3.

resuelto por javier lopez

\;

Sean u = i+2j-3k, v = 2i+3j+k, w = 2i-j+2k y c = -3. verificar

a. (u x v) = -(v x u)

b.u x (v+w) = u x v + u x w

c.(u x v) <with|mode|math|>= (cu) x v = u x (cv)

\;

Solucion a.

(u x v) = -(v x u)

para esto operamos realizamos el producto cruz (u x v) primero.

\

<with|prog-language|sage|prog-session|default|<\session>

<\input|>

u=vector([1,2,-3])

</input>

<\input|>

v=vector([2,3,1])

</input>

<\input|>

x=u.cross_product(v)

</input>

<\input|>

x

</input>

<\output>

<with|mode|math|<left|(>11,-7,-1<right|)>>

</output>

<\input|>

\;

</input>

</session>>

\

ahora operamos \ -(v x u).

<with|prog-language|sage|prog-session|default|<\session>

<\input|>

x=v.cross_product(u)

</input>

<\input|>

x

</input>

<\output>

<with|mode|math|<left|(>-11,7,1<right|)>>

</output>

<\input|>

\;

</input>

</session>>

obtenemos (u x v) = - (v x u)

Solucion b.

u x (v+w) = u x v + u x w

\ u x (v+w)\

\ operamos\

<with|prog-language|sage|prog-session|default|<\session>

<\input|>

w=vector([2,-1,2])

</input>

<\input|>

x=u.cross_product(v+w)

</input>

<\input|>

x

</input>

<\output>

<with|mode|math|<left|(>12,-15,-6<right|)>>

</output>

<\input|>

\;

</input>

</session>>

ahora operamos u x v + u x w.

<with|prog-language|sage|prog-session|default|<\session>

<\input|>

x=u.cross_product(v)+u.cross_product(w)

</input>

<\input|>

x

</input>

<\output>

<with|mode|math|<left|(>12,-15,-6<right|)>>

</output>

\;

</session>>

obtenemos u x (v+w) = u x v + u x w

Solucion c.\

(u x v) <with|mode|math|>= (cu) x v = u x (cv)

del la solucion del a tenemos que (u x v) =

<with|mode|math|<left|(>11,-7,-1<right|)>>, por consiguiente operaremos

\ (cu) x v\

<with|prog-language|sage|prog-session|default|<\session>

<\input|>

c=-3

</input>

<\input|>

x=(c*u).cross_product(v)

</input>

<\input|>

x

</input>

<\output>

<with|mode|math|<left|(>-33,21,3<right|)>>

</output>

<\input|>

\;

</input>

</session>>

ahora operamos u x (cv)

<with|prog-language|sage|prog-session|default|<\session>

<\input|>

<\input|>

x=u.cross_product(c*v)

</input>

<\input|>

x

</input>

<\output>

<with|mode|math|<left|(>-33,21,3<right|)>>

</output>

<\input|>

\;

</input>

</input>

</session>>

\;

Obtenemos (u x v) <with|mode|math|>= (cu) x v = u x (cv)

\;

</body>

Content actions

Download module as:

PDF | More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks