spain-selectividad 2021 QA.3

spain-selectividad · Other · selectividad__madrid_matematicas-II_ordinaria 2.5 marks Vectors: Lines & Planes Multi-Step Geometric Modeling Problem
Let the line $r \equiv \left\{ \begin{array} { l } - x - y + z = 0 \\ 2 x + 3 y - z + 1 = 0 \end{array} \right.$ and the plane $\pi \equiv 2 x + y - z + 3 = 0$. It is requested:\ a) ( 0.75 points) Calculate the angle formed by $r$ and $\pi$.\ b) (1 point) Find the symmetric point of the intersection of line $r$ and plane $\pi$ with respect to the plane $z - y = 0$.\ c) ( 0.75 points) Determine the orthogonal projection of line $r$ onto plane $\pi$.
Let the line $r \equiv \left\{ \begin{array} { l } - x - y + z = 0 \\ 2 x + 3 y - z + 1 = 0 \end{array} \right.$ and the plane $\pi \equiv 2 x + y - z + 3 = 0$. It is requested:\
a) ( 0.75 points) Calculate the angle formed by $r$ and $\pi$.\
b) (1 point) Find the symmetric point of the intersection of line $r$ and plane $\pi$ with respect to the plane $z - y = 0$.\
c) ( 0.75 points) Determine the orthogonal projection of line $r$ onto plane $\pi$.