2 4 1 2 4 2 2 � � � s x y 4 1 4 2 232 Determina el ángulo que forman las rectas

2 4 1 2 4 2 2 ? ? ? s x y 4 1 4 2 232 determina el

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= 2 4 1 2 4 2 2 λ λ λ s x y : = 4 1 4 2
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232 Determina el ángulo que forman las rectas. a) r : s : c) r : b) r : y = 3 x + 2 s : d) r: 20 x 4 y + 1 = 0 a) u r = (3, 2), u s = (2, 3) α = 22° 37 ' 11,51 '' b) u r = (1, 3), u s = ( 4, 8) α = 45° c) u r = (2, 6), u s = ( 1, 2) α = 45° d) u r = (4, 20), u s = (3, 15) α = ¿Qué ángulo forman las rectas? a) r : s : 4 x + 2 y 1 = 0 b) r : s : c) r : s : 2 x + 2 y 1 = 0 d) r : s : e) r : 3 x y 3 = 0 s : f) r : s : x y = + 4 3 6 6 x y = = 2 3 λ x y + = 2 2 4 x y 2 1 3 = + y x = + 6 1 3 x y = = + λ λ 3 y x = 9 8 3 x y + = 1 5 2 y x = 6 4 3 102 cos d c d c d d c c α = + + + = + 1 1 2 2 1 2 2 2 1 2 2 2 4 3 20 1 5 4 20 3 15 312 312 1 2 2 2 2 + + = = cos d c d c d d c c α = + + + = ⋅ − + 1 1 2 2 1 2 2 2 1 2 2 2 2 1 6 ( ) + + = = = = 2 2 6 1 2 10 200 1 2 2 2 2 2 2 2 ( ) cos d c d c d d c c α = + + + = ⋅ − + 1 1 2 2 1 2 2 2 1 2 2 2 1 4 3 ( ) + + = = = 8 1 3 4 8 20 800 2 2 2 2 2 2 ( ) cos d c d c d d c c α = + + + = + 1 1 2 2 1 2 2 2 1 2 2 2 3 2 2 3 3 2 2 3 12 13 2 2 2 2 + + = y x = + 4 1 2 x y 2 4 6 = x y = = + 2 5 3 μ μ x y = = − − 2 3 1 2 λ λ 101 Geometría analítica s : s : 15 x + 3 y + 7 = 0 2 3 1 2 x y + =
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233 a) u r = (3, 6), u s = (2, 4) α = 53° 7 ' 48,37 '' b) u r = (1, 2), u s = (3, 9) α = 8° 7 ' 48,37 '' c) u r = (1, 1), u s = (2, 2) α = 90° d) u r = ( 3, 6), u s = (2, 3) α = 60° 15 ' 18,43 '' e) u r = (1, 3), u s = (2, 4) α = 45° f) u r = ( 1, 0), u s = (3, 6) α = 63° 26 ' 5,82 '' Encuentra el ángulo que forman la recta que pasa por los puntos P ( 1, 4) y Q (3, 8) y la recta . PQ = (4, 4), u r = (2, 8) α = 30° 57 ' 49,52 '' cos d c d c d d c c α = + + + = + 1 1 2 2 1 2 2 2 1 2 2 2 4 2 4 8 4 4 2 8 40 2 176 2 2 2 2 + + = . x y = + 3 2 2 8 103 cos d c d c d d c c α = + + + = + 1 1 2 2 1 2 2 2 1 2 2 2 1 3 0 ( ) + + = = 6 1 0 3 6 3 45 5 5 2 2 2 2 ( ) cos d c d c d d c c α = + + + = + ⋅ − 1 1 2 2 1 2 2 2 1 2 2 2 1 2 3 ( 4 1 3 2 4 10 200 2 2 2 2 2 2 ) ( ) + + − = = cos d c d c d d c c α = + + + = + 1 1 2 2 1 2 2 2 1 2 2 2 3 2 6 3 ( ) + + = = 3 2 6 3 12 585 4 65 65 2 2 2 2 cos d c d c d d c c α = + + + = + ⋅ − 1 1 2 2 1 2 2 2 1 2 2 2 1 2 1 ( 2 1 2 1 2 0 2 2 2 2 ) ( ) + + − = cos d c d c d d c c α = + + + = + 1 1 2 2 1 2 2 2 1 2 2 2 1 3 2 9 1 2 3 9 21 450 21 15 2 7 2 10 2 2 2 2 + + = = = = cos d c d c d d c c α = + + + = + − 1 1 2 2 1 2 2 2 1 2 2 2 3 2 6 ( ) + − + = = 4 3 6 2 4 18 30 3 5 2 2 2 2 ( ) 5 SOLUCIONARIO
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234 Obtén la medida de los ángulos que forman las parejas de rectas. a) r: y s es la recta que pasa por ( 1, 6) y es paralela a 4 x + 2 y + 7 = 0. b) r: y s es la recta que pasa por (3, 8) y es paralela a . c) r: 8 x 2 y 3 = 0 y s es perpendicular a la recta y pasa por (3, 2).
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