spain-selectividad 2023 QB.3

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2 marks Vectors 3D & Lines Multi-Part 3D Geometry Problem
Given the plane $\pi : x + 3 y + 2 z + 14 = 0$ and the line $r \equiv \left\{ \begin{array} { l } x = 2 \\ z = 5 \end{array} \right.$, find:\ a) ( 0.5 points) Find the point on the plane $\pi$ closest to the origin of coordinates.\ b) (1 point) Calculate the orthogonal projection of the OZ axis onto the plane $\pi$.\ c) (1 point) Find the line with direction perpendicular to $r$, contained in $\pi$, and intersecting the OZ axis.
Given the plane $\pi : x + 3 y + 2 z + 14 = 0$ and the line $r \equiv \left\{ \begin{array} { l } x = 2 \\ z = 5 \end{array} \right.$, find:\
a) ( 0.5 points) Find the point on the plane $\pi$ closest to the origin of coordinates.\
b) (1 point) Calculate the orthogonal projection of the OZ axis onto the plane $\pi$.\
c) (1 point) Find the line with direction perpendicular to $r$, contained in $\pi$, and intersecting the OZ axis.