(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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122 CAPÍTULO 11. ¡¤¥ ¥ ¡ ¦£¦¥ ¡ ¤¡¤¥ ¥ £<br />
<br />
<br />
(u × v) | w<br />
= |1 + 1| = 2<br />
¢<br />
¦£¥ ¢ £ ¡¤¥ ¥ <br />
u v w ¡<br />
¡ ¨ ¢ (O; e1, e2, e3) <br />
<br />
<br />
A = (0, k, −3) B = (−1, 0, −4) C = (1, k, −3)<br />
¡<br />
k<br />
¡<br />
C 1<br />
¢ ¡ A B<br />
<br />
<br />
[OA]<br />
[OB] [OC] ¢ k <br />
6<br />
k O A B C £¢ <br />
<br />
<br />
¨¥ ¨ <br />
−→<br />
AB = B − A = (−1, −k, −1)<br />
−→<br />
AC = C − A = (1, 0, 0)<br />
<br />
−→<br />
AB × −→<br />
AC =<br />
¡<br />
¢¢¡<br />
<br />
<br />
<br />
<br />
e1 e2 e3<br />
−1 −k −1<br />
1 0 0<br />
= −e2 + ke3<br />
−→<br />
AB× −→<br />
AC<br />
2<br />
=<br />
<br />
<br />
<br />
= − <br />
√ (−1) 2 +(k) 2<br />
2<br />
−1 −1<br />
1 0<br />
<br />
<br />
e2 +<br />
= √ 1+k 2<br />
2<br />
<br />
<br />
<br />
−1 −k<br />
1 0<br />
<br />
<br />
e3<br />
¢ 1£¢ ¢ <br />
k<br />
√<br />
1+k2 2 = 1 ⇐⇒ 1 + k2 = 4 ⇐⇒ k 2 = 3 ⇐⇒ k = ± √ 3<br />
<br />
−→<br />
OA = A − O = (0, k, −3)<br />
−→<br />
OB = B − O = (−1, 0, −4)<br />
−→<br />
OC = C − O = (1, k, −3)