(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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126 CAPÍTULO 12. £ £ ¥ § § ¤§ ¢¢¡ ¤§<br />
<br />
x−3 y−2<br />
= −2 2<br />
= z+1<br />
−3<br />
−→<br />
AB = B − A = (−1, −1, 1) £¢ R<br />
¡ ¢ £¢ <br />
<br />
R A = (3, 2, −1) B = (2, 1, 0)<br />
R = A + 〈 −→<br />
AB〉 = (3, 2, −1) + 〈(−1, −1, 1)〉<br />
<br />
(x, y, z) ∈ R ⇐⇒ (x, y, z) = (3, 2, −1) + λ(−1, −1, 1) λ ∈ IR<br />
¢ £¢ ¢ ¡ <br />
<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
<br />
x−3<br />
−1<br />
= y−2<br />
−1<br />
x = 3 − λ<br />
y = 2 − λ<br />
z = −1 + λ<br />
= z+1<br />
1 ⇐⇒ 3 − x = 2 − y = z + 1<br />
<br />
R A = (1, 0, ¡ <br />
2) ¢ ¢ 2x − y + z =<br />
0<br />
u = (2, −1, 1)<br />
¡ 2x − y + z = 0£¢ R ¡ u <br />
¢ ¢ <br />
R = A + 〈 −→ u 〉 = (1, 0, 2) + 〈(2, −1, 1)〉<br />
(x, y, z) R ¤ <br />
¥¤ λ ∈ IR <br />
(x, y, z) = (1, 0, 2) + λ(2, −1, 1)<br />
¢ ¢ ¡ <br />
£¢<br />
⎧<br />
⎪⎨ x = 1 + 2λ<br />
y = −λ<br />
⎪⎩<br />
z = 2 + λ