Ivan Tec

/*-ej. de repaso-*/

$\textrm{Siendo }$

$\textrm {M( 2,-1,-3) V(0,1,7) W(1,4,5)}$

$Realizar:$

$\textrm {a) (M X V) X (V X W) }$

$\textrm { (M X V)}$ =

$\begin{bmatrix}{i}&{j}&{k}\\{2}&{-1}&{3}\\{0}&{1}&{7}\end{bmatrix}$

$\textrm {[(-1)(7)-(3)]i - [(2)(7) - (0)]j - [(2)-(0)]k }$

$\textrm {=(-10i, -14j, 2k) }$

$\textrm { (V X W)=}$

$\begin{bmatrix}{i}&{j}&{k}\\{0}&{1}&{7}\\{1}&{4}&{5}\end{bmatrix}$

$\textrm {[(5)-(28)]i - [(0)-(7)]j + [(0)-(1)]k }$

$\textrm {=(-23i, 7j, -1k) }$

$\begin{bmatrix}{i}&{j}&{k}\\{-10}&{14}&{2}\\{-23}&{7}&{-1}\end{bmatrix}$

$\textrm {= [(-14)-(14)]i - [ (10)- (43)]j + [-70+322]k}$

$Resultado$ $\textrm {= (-28i, -46j, 252k)}$

$b)$

$V X (V-2W)$ $=$

$\textrm {<br>=V X [(0,1,7) - 2(1,4,5)] }$

$\textrm {<br>=V X [(0,1,7) - ( 2, 8, 10)] }$

$\textrm {<br>=V X [(-2,-7,-3)]}$

$\textrm {<br>=(0,1,7) X (-2,-7,-3)}$

$\begin{bmatrix}{i}&{j}&{k}\\{0}&{1}&{7}\\{-2}&{-7}&{-3}\end{bmatrix}$

$\textrm {= [-49+3]i - [0+14]j + [0+2]k }$

$\textrm {Resultado = (-46i, -14j, 2k)}$

$c)$

$\textrm {(MxV)-2W = }$

$\textrm { (M X V)}$ =

$\begin{bmatrix}{i}&{j}&{k}\\{2}&{-1}&{3}\\{0}&{1}&{7}\end{bmatrix}$

$\textrm {[(-1)(7)-(3)]i - [(2)(7) - (0)]j - [(2)-(0)]k }$

$\textrm {=(-10i, -14j, 2k) }$

$2W = (2,8,10)$

$\begin{bmatrix}{i}&{j}&{k}\\{-10}&{-14}&{2}\\{2}&{8}&{10}\end{bmatrix}$

$\textrm {= [16+140]i - [-100-14]j + [ -80+28] }$

R $\textrm{=(124i, -104j, -52k)}$

Ivan Tec

martes, 16 de septiembre de 2008

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