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x − 1 = y−2<br />

2<br />

= z − 3<br />

<br />

u = (1, 1)<br />

2, v = (2, 1) ¢ <br />

2, P A = (1, 3) ¡ u 2, v<br />

£¢ ¢ <br />

P = A + 〈u, v〉 = (1, 2, 3) + 〈(1, 2, 1), (2, 2, 1))〉<br />

¢ P ¡<br />

(x, y, z) = (1, 2, 3) + λ(1, 2, 1) + µ(2, 2, 1), λ, µ ∈ IR<br />

⎧<br />

⎪⎨<br />

¡ <br />

<br />

x = 1 + λ + 2µ<br />

⎪⎩<br />

y = 2 + 2λ + 2µ<br />

z = 3 + λ + µ<br />

λ, µ ∈ IR<br />

λ µ <br />

¥<br />

(x, y, z) ∈ P ⇐⇒ 1<br />

2<br />

(y − 2) = z − 3 ⇐⇒ y − 2z + 4 = 0<br />

171

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