1. Encontre o produto interno −→ u • −→v nos casos abaixo: (a) −→ u = ( 2, 1 ) e −→ v = ( −4, 2 ) (b) −→ u = ( −1, 4 ) e −→ v = (√ 3, √ 2 ) (c) −→ ...
1. Encontre o produto interno
−→
u • −→v nos casos abaixo:
(a)
−→
u =
(
2, 1
)
e
−→
v =
(
−4, 2
)
(b)
−→
u =
(
−1, 4
)
e
−→
v =
(√
3,
√
2
)
(c)
−→
u =
(
−2, 0
)
e
−→
v =
(
3,−1
)
(d)
−→
u =
(
4, 3
)
e
−→
v =
(
4, 5
)
(e)
−→
u =
(
4, 7, 3
)
e
−→
v =
(
2, 1, 1
)
(f)
−→
u =
(
0,−5, 2
)
e
−→
v =
(
3, 2,−6
)
(g)
−→
u =
(
7, 1,−7
)
e
−→
v =
(
0, 1,−1
)
(h)
−→
u =
(
−2,−1, 3
)
e
−→
v =
(
−4, 3,−1
)
−→
u • −→v nos casos abaixo:
(a)
−→
u =
(
2, 1
)
e
−→
v =
(
−4, 2
)
(b)
−→
u =
(
−1, 4
)
e
−→
v =
(√
3,
√
2
)
(c)
−→
u =
(
−2, 0
)
e
−→
v =
(
3,−1
)
(d)
−→
u =
(
4, 3
)
e
−→
v =
(
4, 5
)
(e)
−→
u =
(
4, 7, 3
)
e
−→
v =
(
2, 1, 1
)
(f)
−→
u =
(
0,−5, 2
)
e
−→
v =
(
3, 2,−6
)
(g)
−→
u =
(
7, 1,−7
)
e
−→
v =
(
0, 1,−1
)
(h)
−→
u =
(
−2,−1, 3
)
e
−→
v =
(
−4, 3,−1
)
💡 1 Resposta
Ed 
Para encontrar o produto interno entre dois vetores, precisamos multiplicar as componentes correspondentes de cada vetor e somar os resultados. Assim, temos: (a) −→u • −→v = (2)(-4) + (1)(2) = -8 + 2 = -6 (b) −→u • −→v = (-1)(√3) + (4)(√2) = -√3 + 4√2 (c) −→u • −→v = (-2)(3) + (0)(-1) = -6 (d) −→u • −→v = (4)(4) + (3)(5) = 16 + 15 = 31 (e) −→u • −→v = (4)(2) + (7)(1) + (3)(1) = 8 + 7 + 3 = 18 (f) −→u • −→v = (0)(3) + (-5)(2) + (2)(-6) = 0 - 10 - 12 = -22 (g) −→u • −→v = (7)(0) + (1)(1) + (-7)(-1) = 0 + 1 + 7 = 8 (h) −→u • −→v = (-2)(-4) + (-1)(3) + (3)(-1) = 8 - 3 - 3 = 2 Portanto, as respostas são: (a) -6 (b) -√3 + 4√2 (c) -6 (d) 31 (e) 18 (f) -22 (g) 8 (h) 2
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