(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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x−1<br />
<br />
2<br />
= y<br />
−1<br />
= z−2<br />
<br />
u = (2e1 − 3e2) × (e1 + e2 + e3) =<br />
=<br />
<br />
<br />
<br />
−3 0<br />
1 1<br />
<br />
<br />
e1 −<br />
1<br />
<br />
<br />
<br />
2 0<br />
1 1<br />
⇐⇒ x − 1 = −2y = 2(z − 2)<br />
<br />
<br />
e2 +<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
2 −3<br />
1 1<br />
<br />
<br />
<br />
<br />
<br />
<br />
e3 = −3e1 − 2e2 + 5e3<br />
e1 e2 e3<br />
2 −3 0<br />
1 1 1<br />
R A = (1, 0, 2) ¡ u <br />
¢ <br />
£¢<br />
R = A + 〈u〉 = (1, 0, 2) + 〈(−3, −2, 5)〉<br />
<br />
(x, y, z) ∈ R ⇐⇒ (x, y, z) = (1, 0, 2) + λ(−3, −2, 5), λ ∈ IR<br />
⎧<br />
⎪⎨<br />
¢ ¡ ¢¡<br />
⎪⎩<br />
x = 1 − 3λ<br />
y = −2λ<br />
z = 2 + 5λ<br />
¢<br />
<br />
x−1<br />
−3<br />
= y<br />
−2<br />
= z−2<br />
5<br />
¡ ¨ £¢ <br />
¢ ¡ ©<br />
<br />
<br />
x = 0 y =<br />
<br />
3z<br />
<br />
2x + y + z = 1 x − y − z + 2 = 0<br />
<br />
¨¥ ¨ R ¢ ¡ ©<br />
<br />
x = 0 y = 3z<br />
£¢<br />
(x, y, z) ∈ R ⇐⇒ (x, y, z) = (0, 3z, z) = z(0, 3, 1)<br />
<br />
127
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