Gonzalo.....

$\mu = (2, -1, 3)\\ V = (o, 1, 7)\\ X = (1,4, 5)\\ a) ( \mu x V) x ( V x W)\\ b) \mu x (V -2W)\\ c) ( \mu x V) - 2W\\$

i j k
2 -1 3
0 1 7

$[(-1)(7)\;-\;(1)(3)]\;-\;[(2)(7)\;-\;(0)(3)]\;+\;[(2)(1)\;-\;(0)(-1)]\\(-7-3)\;-\;(14)\;+\;(2)$
$-10i\:-14j\:+\:2k$

i j k
0 1 7
1 4 5

$[(1)(7)\:-(4)(7)]i\:-\:[(0)(5)\:-(1)(7)]j\:+[(0)(4)\:-(1)(1)\\ (7-28)\:-(0-7)\:(0-1)]k$

$-21i\:+7j\:-1k$

i j k
$-10i\:-14j\:+\:2k$
$-21i\:+7j\:-1k$

$[(14)(1)\:-(7)(2)]i\:[(10)(1)\:-(21)(2)]j\:+[(10)(7)\:-(21)(14)]k$

b) $\mu\:x\:(V-2W)$

i j k
o 1 7
2 8 10

$[(1)(10)\:-(8)(7)]i\:[(0)(10)-(2)(7)]j\:+[(0)(8)-(2)(7)]k\\ (10-56)-(0-14)+(0-14)\\ -46, 14, -14$

i j k
-46 14 -14
2 -1 3

$[(1)(10)\:-(8)(7)]i\:[(0)(10)-(2)(7)]j\:+[(0)(8)-(2)(7)]k\\ (10-56)-(0-14)+(0-14)\\ -46, 14, -14$

i j k
2 -1 3
-46 14 -14

$[(-1)(14)- (14)(3)]i - [(2)(14)- (46)(3)]+[(2)(14)-(46)(-1)\\ (-14 - 42)- (28 - 138) + (28 - 46)\\ -56, -14, 74$

C) $(\mu x V) - 2 w$

i j k
2 -1 3
0 1 7

$[(-1)(7) - (1)(3)]-[(2)(7)-(0)(3)]+[(2)(1)-(0)(-1)\\ (-7-3) - (14 -3) + (2+1)\\ -10, -11, 3 -10 -11 3\\ 2\:(1 , 4 , 5)\\ \\ -10 -11 3 \\ \:2 \: 8 \: 10\\ \\ = -8 -3 -7$

Gonzalo.....

lunes, 1 de septiembre de 2008

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