Trabalho

Portfólio de Álgebra e Calculo Vetorial

7˚ Semestre

Prof.

Guarulhos
2012

FACULDADE ENIAC

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Guarulhos
2012

1) Dados os vetores u = 2i – 3j, v = i – j e w = -2i + j, determinar.
a) 2u – v
→ 2(2i – 3j) – (i-j) = (4i – 6j) – (i-j)
→ = (3i – 5j)
b) v – u + 2w
(i – j) – (2i – 3j) + 2(-2i + j) = (-i + 2j) + (-4i + 2j) = (-5i + 4j)
c) 1/2u -2v – w ½(2i – 3j) – 2(i – j) – (-2i + j) = (1i – 1,5j) – 2i + 2j + 2i –j = (1i – 0,5j)
d) 3u – 1/2v – 1/2w 3(2i-3j) – ½(i–j) – ½(-2i + j) = 6i – 9j – 0,5i + 0,5j + 1i – 0,5j = (6,5i – 9j)

2) Dados os vetores u=(3,-1) e v=(-1,2), determinar o vetor x tal que.
a) 4(u-v) + 1/3x = 2u – x
4(3-(-1)+1/3x=2U-x
16+x/3=6-x
48+x=18-3x
4x=18-48
4x=-30
x=-15/2
4((-1)-2)+x/3=2.(-1)-x
-12+x/3=2-x
-36+x=-6-3x
4x=30 x=15/2 X=(-15/2,15/2)

b) 3x – (2v – u) = 2(4x – 3u)
3x-(2.(-1)-3)=2.(4x-3.3)
3x+5=8x-18
-5x=-23
x=23/5

3x-(2.2-(-1))=2(4x-3.(-1)
3x-5=8x+6
-5x=11 x=-11/5 X=(23/5,-11/5)

3) Dados os pontos A(-1,3), B(2,5), C(3,-1) e O(0,0), calcular.
a) OA – AB
OA
O(0,0) – OAi (0-(-1)) = +1
A(-1,3) – OAj (0-3) = -3
OA = +1i-3j
AB
A(-1,3) – ABi (2-(-1)) = 3
B( 2,5) – ABj (5 - 3) = 2
AB = 3i + 2j inverter → BA = -3i – 2j
OA = +1i-3j
BA = -3i – 2j

→ OB = -2i – 5j
b) OC – BC
OC
O(0,0) – OCi (3 - 0) = 3
C(3,-1) – OCj (-1 - 0) = -1 OC = 3i – 1j
BC
B(2,5) – BCi (3 - 2) = 1
C( 3,-1) – BCj (-1 -5) = -6 BC = 1i - 6j inverter → CB = -1i + 6j

OC = 3i – 1j
CB = -1i + 6j
→ OB = 2i +5j

c) 3BA – 4CB
BA
B(2,5) – BAi (-1 - 2) = - 3
A(-1,3) – BAj (3 - 5) = -2