Hampton Rowe
07/11/2023 · Primary School
2. Sean las rectas: \( r:\left\{\begin{array}{l}x=-2+3 \lambda \\ y=1-\lambda \\ z=2 \lambda\end{array}\right. \) y \( \quad r^{\prime}:\left\{\begin{array}{l}y=3 x-13 \\ z=4\end{array}\right. \) a) Verificar que \( r \) y \( r^{\prime} \) son perpendiculares y secantes en un punto \( Q \); hallar \( Q \) b) Dar la ecuación general de un plano \( \pi \) que sea paralelo a ambas rectas y pase por el punto (1,0,2) c) Decidir, justificando adecuadamente, si \( r \) está incluida en \( \pi \)
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a) Las rectas \( r \) y \( r^{\prime} \) son perpendiculares y se intersectan en el punto \( Q(4, -1, 4) \).
b) La ecuación del plano \( \pi \) es \( 6x - 9z + 12 = 0 \).
c) La recta \( r \) está incluida en el plano \( \pi \).
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