Spencer Marsh
09/30/2023 · High School

70 Teniendo en cuenta la recta \( r \equiv \frac{x-1}{-4}=\frac{y-2}{3}=z-3 \) y el plano \( \pi \equiv 3 x+4 y-6=0 \) : a. Comprueba que recta y plano son paralelos. b. Determina dos rectas distintas que estén contenidas en el plano \( \pi \) y sean paralelas a \( r \).

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La recta y el plano son paralelos. Dos rectas contenidas en el plano \( \pi \) y paralelas a \( r \) son: \( \vec{r_1}(t) = (2 - 4t, 3t, 3 + t) \) y \( \vec{r_2}(s) = (-4s, 1.5 + 3s, 3 + s) \).

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