Ejercicios 2

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Abel Cordero Salgado
IC43122
Álgebra
1er semestre
Ingeniería civil
Universidad del Valle de Puebla
Ejercicios
1) 3A – 2B = ((3) (-1/3, 2, -1)) – ((2) (-3, -1, 4) = (-1, 6, -3) – (-6, -2, 8) = (5, 8, -11)
2) -(A/3) + (C/2) + ((3)(B) = (1/9, -2/3, 1/3) + (-1/4, -1/6, 1/8) + (-9, -3, 12) = 
(-5/36, -5/6, 11/24) + (-9, -3, 12) = (-329/36, -23/6, 299/24)
3) Dirección B, desplazamiento 2A
B = (-3, -1, 4)
2A = (2) (-1/3, 2, -1) = (-2/3, 4, -2)
x - (-2/3) / 5 = y – 4 / -1 = z – (-2) / 4
x + 2/3 / 5 = y -4 / -1 = z +2 / 4
4) Dirección -C, desplazamiento 3A + 2C
-C = (1/2, 1/3, -1/4)
3A + 2C = ((3) (-1/3, 2, -1) + ((2) (-1/2, -1/3, 1/4)) = (-1, 6, -3) + (-1, -2/3, 1/2) =
(-2, 16/3, -5/2)
x + 2 / 1/2 = y - 16/3 / 1/3 = z + 5/2 / -1/4
5) Punto del plano -A, vector perpendicular B – C/2
-A = - (-1/3, 2, -1)
-A = (1/3, -2, 1)
B – C/2 = (-3, -1, 4) - ((-1/2, -1/3, 1/4) /2)
B -C/2 = (-3, -1, 4) – (-1/4, -1/6, 1/8)
B – C/2 = (-11/4, -5/6, 33/8)
-1/4 (x – 1/3) – 5/6 (y + 2) + 33/8 (z -1) = 0
6) Punto del plano 2B+ C, vector perpendicular -B +A
2B+C= 2 (-3, -1, 4) + ( -1/2, -1/3, 1/4) = (-6, -2, 8) + (-1/2, -1/3, 1/4) =
(-13/2, -7/3, 33/4)
-B + A = - (-3, 1, 4) + (-1/3, 2, -1) = (8/3, 1, -5)
8/3 (x +13/2) + 1 (y + 7/3) – 5 (z – 33/4) = 0