Karteikarten
fórmulas Espacio vectorial
Karten in diesem Stapel (8)
- 1suma de vectores\[(a_1,a_2,a_3)\pm(b_1,b_2,b_3)=(a_1\pm b_1,a_2\pm b_2,a_3\pm b_3)\]
- 2producto de un nº real por un vector\[k.(a_1,a_2,a_3)=(k.a_1,k.a_2,k.a_3)\]
- 3Producto Escalar\[u.v=a.a'+b.b'+c.c'\]
\[u.v=\left|u\right|\left|v\right|.\cos\left(\alpha\right)\]
\[\overset\rightharpoonup u.\overset\rightharpoonup v=0\Leftrightarrow\overset\rightharpoonup u\perp\overset\rightharpoonup v\]
\[u=k.v\Leftrightarrow u\parallel v\] - 4Módulo de un vector\[\left|(a,b,c)\right|=\sqrt{a^2+b^2+c^2}\]
- 5Producto Vectorial\[uxv\ =\begin{vmatrix}\overset\rightharpoonup i&\overset\rightharpoonup j&\overset\rightharpoonup k\\a&b&c\\a'&b'&c'\end{vmatrix}=\left(\begin{vmatrix}b&c\\b'&c'\end{vmatrix},-\begin{vmatrix}a&c\\a'&c'\end{vmatrix},\begin{vmatrix}a&b\\a'&b'\end{vmatrix}\right)\]
\[\left|u\times v\right|=\left|u\right|.\left|v\right|.\sin\left(\alpha\right)=área\;del\;paralelogramo\;que\;forman\] - 6Producto Mixto\[\left[u,v,w\right]=\begin{vmatrix}a&b&c\\a'&b'&c'\\a''&b''&c''\end{vmatrix}=volúmen\;del\;paralelepípedo\;que\;forman\]
- 7Punto Medio de un Segmento\[\begin{array}{l}A=(x_0,y_0,z_0)\;\;B=(x_1,y_1,z_1)\\\overset\rightharpoonup{AB\;}M=\left(\frac{x_0+x_1}2,\frac{y_0+y_1}2,\frac{z_0+z_1}2\right)\end{array}\]
- 8Puntos alineados\[\begin{array}{l}\frac{a'-a}{a''-a'}=\frac{b'-b}{b''-b'}=\frac{c'-c}{c''-c'}\\\end{array}\]
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- Bachillerato Matematicas Karteikarten am fórmulas Espacio vectorial, erstellt von Pello López am 11/03/2016.
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- Pello López
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