Ficha De Matematica Para Fisicos

Cacilda Tamele
Lúcia Agostinho Sitoe
Silva Fenias Cuinica
Zefanias Ivaristo Mboa

Matemática para físicos I

Licenciatura em Ensino de Física

Universidade Pedagógica Gaza
Xai – Xai

Resolução da ficha 1
1. Achar + , Se:
a) = (1,3,0,-1) e = (0,4,-1,3) b) = (3x, y, x+y) e = (0, -y, -x) + = (1,3,0,-1) + (0,4,-1,3) + = (3x, y, x + y) + (0, -y, -x) + = (1+0, 3+4, 0-1, -1 + 3) + = (3x+0, y-y, x+y-x) + = (1,7,-1,2) + = (3x,0,y)
.c) = (1,3,0,) e = (2,4) + = (1,3,0,) + (2,4) + = (1+2,3+4,0) + = (3,7,0)
2. Determine os vectores e sendo:
a) = (x+y, 3x-y), = (2x,y-2x), + = (5,1)
(x+y, 3x-y) + (2x,y-2x) = (5,1)
(3x+y,x) = (5,1) Então = (3,1) e = (2,0)

b) = (x + y, x-y), = (x+2y,2y-2), - = (-1,1)
(x + y, x-y) - (x+2y,2y-2) = (-1,1)
(-y,x-3y+2) = (-1, 1) Então = (3, 1) e = (4,0)

c) = (x, y,z), = (y,z,x), = (z,-x,y), 2--3 = (-9,4,-1)
2(x,y,z) – (y,z,x) – 3(z,-x,y) = (-9,4,-1)
(2x-y-3z,2y-z+3x,2z-x-3y) = (-9,4,-1) = (2,1,2), = (1,2,2) e = (2,-2,1).

3. A combinação linear 2 - + 3 = (11,-4,3) e sabe-se que estes vectores têm a forma = (3x,0,y), = (y,z,x) e = (2y+z, x-y, 0), determina-los.
2(3x,0,y) – (y,z,x) + (2yz,x-y,0) = (11,-4,3)
(6x -y+2yz, 0-z+x-y, 2y-x+0) = (11,-4,3) As coordenadas serão: = (2,0,), = (,,) e = (, , 0).

4. Calcular 2- 4 + 3 sendo:
a) = (1,0,1), = (1,1,0) e = (1,-1,2)
2- 4 + 3 = 2(1,0,1) - 4(1,1,0) + 3(1,-1,2)
2- 4 + 3 = (-2,-4,5)

b) = (1,-1,3), = (2,3,-1) e = (0,0,1)
2- 4 + 3 = 2(1,-1,3) - 4(2,3,-1) + 3(0,0,1)
2- 4 + 3 = (-3,-17,16)

c) = (1,2,-2) e = (6,3,-2)
2- 4 + 3 = 2(1,2,-2) - 4(6,3,-2)
2- 4 + 3 = (-22,-8,4)
5. Calcular o comprimento do vector , se:
a) = (1, 2,-2) b) = (6, 3,-2)