Hello, I'm having trouble with problem 11 c & d. In my approach to solving the equations in c, I have too many unknowns to solve. My teacher gave me the tip to think of values for some numbers and then plug them into two coordinates. However, I can't seem to implement this in the problem. Maybe someone can help me! (Note: at b=9 and d=0.75, the direction vectors are collinear)
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Schrittweise vorgehen:
Setze (c│0│3) als Schnittpunkt. Das führt zu:
(1) 1 + r * b = c
(2) a + 3 * r = 0
(3) 2 + 4 * r = 3
———————
(3) r = 1 / 4
(2) a = -3 / 4
(1) c = (b / 4) + 1
Parallelität ausschließen:
Richtungsvektoren sind parallel, wenn gilt:
(1) (1 / 4) * b = 3 * s
(2) (1 / 4) * 3 = s
(3) (1 / 4) * 4 = s * d
————————
(2) s = 3 / 4
(1) b = 9
(3) (1 / 4) * 4 = (3 / 4) * d ⇒ d = 3 / 4
Folglich ist d ≠ 3 / 4 , wenn die Richtungsvektoren nicht parallel verlaufen.
Wenn b = 9 , so ist c = 13 / 4
Den richtungsvektor von h kannst du rauslassen und a,b und c so bestimmen, das g h am “stützvektorpunkt” (c, 0, 3) von h schneidet
wie das ?