(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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138 CAPÍTULO 13. £ £ ¥ § § ¤§ ¢¢¡ ¤§<br />
¡ ¨ P ¢ ¢ <br />
<br />
x + αy + 2z + β = 0, α, β ∈ IR<br />
R ¢ <br />
<br />
(x, y, z) = (1, 0, 0) + λ(1, α, 2), λ ∈ IR<br />
R P<br />
<br />
<br />
P ′ <br />
¢ <br />
<br />
(x, y, z) = (1, 1, −1) + λ(0, 1, −1) + µ(4, −1, −1), λ, µ ∈ IR<br />
α β ′ d (P, P ) = 3<br />
<br />
<br />
¥¤<br />
(x0, y0, <br />
z0)<br />
(x0, y0, z0) = (1, 0, 0) + λ0(1, α, 2) = (1 + λ0, αλ0, 2λ0)<br />
¨¥ ¨ R ¡ P ¡ <br />
<br />
£¢ ¤ λ0<br />
¢ <br />
<br />
λ0(1 + α 2 ) + β + 1 = 0 ⇐⇒ λ0 = − β+1<br />
α2 +5<br />
¢ P R ¡ <br />
<br />
(x0, y0, z0) =<br />
<br />
1 − β+1<br />
α 2 +5<br />
, − (β+1)α<br />
α 2 +5<br />
d (R, P) = 0<br />
<br />
′ ¢ <br />
P<br />
2β+2<br />
, − α2 <br />
+5<br />
(x, y, z) = (1, 1, −1) + λ(0, 1, −1) + µ(4, −1, −1), λ, µ ∈ IR<br />
′ d (P, P ) = 3 P ′ P <br />
P ′¡<br />
P <br />
∈ IR <br />
<br />
<br />
§<br />
u = (0, 1, −1) × (4, −1, −1) = (−2, −4, −4) v = (1, α, ¢ <br />
2)